Class 12 : Physics (English) – Chapter 1: Electric Charges and Fields

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On June 25, 2025

EXPLANATION & SUMMARY

Introduction to Electrostatics
Electricity begins with the concept of electric charge. Electrostatics is the study of charges at rest. This chapter lays the foundation for understanding the forces, fields, and principles associated with electric charges.

Electric Charge and Its Properties
Electric charge is a fundamental property of matter, just like mass. It exists in two forms: positive and negative. Charges of the same kind repel each other, while unlike charges attract.

Key Properties of Electric Charge:
Additivity: Charges can be added algebraically. For example, +2C and -3C result in -1C total charge.
Conservation: Total electric charge is conserved in an isolated system. Charge can neither be created nor destroyed, only transferred.
Quantization: Charge exists in discrete packets, i.e., it is quantized. The smallest unit is the charge of an electron (e = 1.6 × 10⁻¹⁹ C). Any charge (q) = ne, where n is an integer.
Invariance: Electric charge is unaffected by the state of motion. It remains the same in all reference frames.

Methods of Charging a Body
Friction: Rubbing two different materials transfers electrons, e.g., rubbing glass with silk.
Conduction: Charging by direct contact between a charged and a neutral body.
Induction: A charged body induces opposite charge on a nearby conductor without touching it.

Coulomb’s Law
Coulomb’s law gives the force between two point charges:
F = (1/4πε₀) × (q₁q₂/r²)

Where:
F = force between charges
q₁ and q₂ = magnitudes of two point charges
r = distance between the charges
ε₀ = permittivity of free space = 8.854 × 10⁻¹² C²/N·m²

This law shows:
The force is directly proportional to the product of charges.
Inversely proportional to the square of the distance.
It acts along the line joining the charges.

Vector Form of Coulomb’s Law
The vector form of force F on charge q₁ due to q₂ is:
F₁₂ = (1/4πε₀) × (q₁q₂/|r₁₂|³) × r₁₂
Where r₁₂ is the position vector from q₁ to q₂.
This law satisfies Newton’s third law: F₁₂ = -F₂₁

The Principle of Superposition
In systems with more than two charges, total force on a charge is the vector sum of all individual forces.
If multiple charges q₁, q₂, q₃, …, qₙ exert forces F₁, F₂, …, Fₙ on charge q, then:
F_total = F₁ + F₂ + … + Fₙ
This principle allows calculation of net force even in complex charge configurations.

Electric Field
The electric field is the region around a charge where other charges feel a force.
Electric Field due to a Point Charge q:
E = (1/4πε₀) × (q/r²) r̂

Where:
E is the electric field vector
r̂ is a unit vector from charge to the point of observation
It is a vector quantity and follows superposition principle.

Electric Field Lines
Visual representation of the electric field:
Begin on positive and end on negative charges
Never intersect
Denser lines = stronger field
Tangent to a field line = direction of electric field
For a single positive charge: radial outward lines
For a dipole: lines curve from positive to negative

Electric Dipole
A pair of equal and opposite charges (+q and -q) separated by a small distance 2a.
Dipole Moment (p) = q × 2a
It is a vector directed from -q to +q.

Electric Field Due to a Dipole
At an axial point (on the line joining charges):
E_axial = (1/4πε₀) × (2p/r³)
At an equatorial point (perpendicular bisector):
E_equatorial = (1/4πε₀) × (p/r³)
Both fields vary as 1/r³ and show directionality based on the position.

Torque on a Dipole in Uniform Electric Field
When placed in a uniform electric field E, a dipole experiences a torque τ:
τ = p × E
Magnitude: τ = pE sinθ
This torque tends to align the dipole along the field direction.

Electric Flux
Electric flux (Φ_E) is the total number of electric field lines crossing a given area.
Φ_E = E · A = EA cosθ
It is a scalar and depends on field strength, area, and angle.

Gauss’s Law
Gauss’s Law relates the total electric flux through a closed surface to the enclosed charge:
∮ E · dA = q_enclosed / ε₀
This law is very useful for calculating electric fields in symmetric charge distributions.

Applications of Gauss’s Law
Electric Field due to a Point Charge
Using a spherical Gaussian surface:
E × 4πr² = q/ε₀ ⇒ E = (1/4πε₀) × (q/r²)
Same result as Coulomb’s law.
Field due to an Infinite Line Charge
Linear charge density λ:
E = λ / (2πε₀r)
Field due to an Infinite Plane Sheet of Charge
Surface charge density σ:
E = σ / (2ε₀)
Field due to Two Parallel Sheets (Oppositely Charged)
Net field between plates = σ/ε₀, and zero outside.

Charge Distribution and Conductors
Inside a conductor, the electric field is zero.
Excess charge resides on the outer surface.
Electric field is perpendicular to surface.
Surface charge distributes uniformly on a spherical conductor.

Cavity Inside a Conductor
Electric field inside a cavity with no charge = 0
If a charge is placed inside the cavity, an opposite charge is induced on the inner surface, and an equal charge on the outer surface.

Important Definitions Recap
Charge (q): Basic unit of electricity
Electric Field (E): Force per unit positive test charge
Electric Dipole Moment (p): q × 2a
Electric Flux (Φ): E × A cosθ
Permittivity (ε₀): Constant describing medium’s ability to permit electric field lines

✍ SUMMARY
Electric charge is a basic property of matter, existing in two types: positive and negative. It follows conservation, quantization, and additivity.
Charging can be done via friction, conduction, or induction.

Coulomb’s Law gives the electrostatic force between two point charges: F = (1/4πε₀)(q₁q₂/r²). It is central to electrostatics.
Electric field (E) at a point is the force per unit charge: E = (1/4πε₀)(q/r²). It is a vector and obeys superposition.
Field lines help visualize the direction and strength of electric fields. Denser lines indicate stronger fields.

An electric dipole consists of two equal and opposite charges separated by a distance. It has a dipole moment p = q × 2a.
Dipoles create electric fields that vary as 1/r³. In uniform electric fields, they experience torque τ = pE sinθ.
Electric flux (Φ) is the number of field lines crossing a surface: Φ = E·A = EA cosθ.

Gauss’s Law states: The total flux through a closed surface equals q_enclosed / ε₀. It simplifies electric field calculations in symmetric cases.
Using Gauss’s Law:
Field due to a point charge: E = (1/4πε₀)(q/r²)
Infinite line: E = λ/(2πε₀r)
Infinite plane sheet: E = σ/(2ε₀)
Between oppositely charged plates: E = σ/ε₀

Inside conductors, the electric field is zero and excess charge resides on the outer surface.
Electric shielding is achieved using conductors. The field inside a cavity remains zero if it contains no charge.
This chapter builds the foundation for all electrostatic phenomena, including electric potential and capacitors.

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TEXTBOOK QUESTIONS

Question 1.1
What is the force between two small charged spheres having charges of 2 × 10⁻⁷ C and 3 × 10⁻⁷ C placed 30 cm apart in air?

Solution:
Given:
q1 = 2 × 10⁻⁷ C
q2 = 3 × 10⁻⁷ C
r = 30 cm = 0.3 m
Coulomb’s law:
F = (1/4πε₀) × (q1 × q2)/r²
where 1/4πε₀ = 9 × 10⁹ N·m²·C⁻²
F = (9 × 10⁹) × (2 × 10⁻⁷ × 3 × 10⁻⁷)/(0.3)²
F = (9 × 10⁹) × (6 × 10⁻¹⁴)/0.09
F = 6 × 10⁻³ N
Answer: 6 × 10⁻³ N (repulsive)

Question 1.2
The electrostatic force on a small sphere of charge 0.4 μC due to another small sphere of charge –0.8 μC in air is 0.2 N. (a) What is the distance between the two spheres? (b) What is the force on the second sphere due to the first?

Solution:
(a) Given:
q1 = 0.4 μC = 4 × 10⁻⁷ C
q2 = –0.8 μC = –8 × 10⁻⁷ C
F = 0.2 N
Coulomb’s law:
F = (1/4πε₀) × |q1 × q2|/r²
0.2 = (9 × 10⁹) × (3.2 × 10⁻¹³)/r²
r² = (9 × 10⁹ × 3.2 × 10⁻¹³)/0.2 = 0.0144
r = √0.0144 = 0.12 m
(b) By Newton’s third law, the force on the second sphere is also 0.2 N (attractive).
Answer: (a) 0.12 m, (b) 0.2 N (attractive)

Question 1.3
Check that the ratio ke²/Gmₑmₚ is dimensionless. Determine its value. What does it signify?

Solution:
k = 1/4πε₀ (units: N·m²·C⁻²), e (C), G (N·m²·kg⁻²), mₑ and mₚ (kg)
ke² has units [ML³T⁻²], Gmₑmₚ also [ML³T⁻²], so the ratio is dimensionless.
k = 8.99 × 10⁹ N·m²·C⁻²
e = 1.602 × 10⁻¹⁹ C
G = 6.67 × 10⁻¹¹ N·m²·kg⁻²
mₑ = 9.11 × 10⁻³¹ kg, mₚ = 1.67 × 10⁻²⁷ kg
Ratio = (8.99 × 10⁹ × (1.602 × 10⁻¹⁹)²) / (6.67 × 10⁻¹¹ × 9.11 × 10⁻³¹ × 1.67 × 10⁻²⁷) ≈ 2.27 × 10³⁹
This ratio compares the electrostatic and gravitational forces between a proton and an electron.
Answer: Dimensionless, value ≈ 2.27 × 10³⁹, signifies electrostatic force is much stronger than gravitational force.

Question 1.4
(a) Explain the meaning of the statement ‘electric charge of a body is quantised’.
(b) Why can one ignore quantisation of electric charge when dealing with macroscopic charges?

Solution:
(a) Electric charge exists in discrete packets; the smallest possible charge is e = 1.6 × 10⁻¹⁹ C. Any charge q = n·e, where n is an integer.
(b) For macroscopic charges (e.g., 10⁻⁶ C), n is extremely large (~10¹³), so the discrete nature is negligible and charge can be treated as continuous.
Answer: (a) Charge is an integer multiple of e. (b) For large n, quantisation is negligible.

Question 1.5
When a glass rod is rubbed with a silk cloth, charges appear on both. Explain how this is consistent with the law of conservation of charge.

Solution:
Rubbing transfers electrons from the glass rod to the silk. The glass loses electrons (becomes positively charged), silk gains electrons (becomes negatively charged). The total charge before and after remains zero.
Answer: Charge is conserved because the total charge of the system remains unchanged; electrons are transferred, not created or destroyed.

Question 1.6
Four point charges qA = 2 μC, qB = –5 μC, qC = 2 μC, and qD = –5 μC are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of 1 μC placed at the centre of the square?

Solution:
Distance from centre to each corner = (10√2)/2 = 5√2 cm = 0.05√2 m
By symmetry, the forces from charges of equal magnitude and opposite sign cancel each other out.
Net force on the central charge is zero.
Answer: 0 N

Question 1.7
(a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
(b) Explain why two field lines never cross each other at any point.

Solution:
(a) Electric field is continuous; a break would imply the field is undefined or zero at that point, which is not possible.
(b) If two field lines crossed, the field at that point would have two directions, which is impossible.
Answer: (a) Field lines must be continuous because the field is continuous. (b) Field lines never cross because the field has a unique direction at any point.

Question 1.8
Two point charges qA = 3 μC and qB = –3 μC are located 20 cm apart in vacuum.
(a) What is the electric field at the midpoint O of the line joining the charges?
(b) If a test charge of 1.5 × 10⁻⁹ C is placed at O, what is the force experienced by it?

Solution:
(a) Distance from O to each charge = 10 cm = 0.1 m
Field due to qA: EA = (9 × 10⁹ × 3 × 10⁻⁶)/(0.1)² = 2.7 × 10⁶ N/C (away from A)
Field due to qB: EB = (9 × 10⁹ × 3 × 10⁻⁶)/(0.1)² = 2.7 × 10⁶ N/C (toward B, which is also away from A)
Net field at O: E = EA + EB = 5.4 × 10⁶ N/C (from A to B)
(b) Force on test charge: F = q × E = 1.5 × 10⁻⁹ × 5.4 × 10⁶ = 8.1 × 10⁻³ N (from A to B)
Answer: (a) 5.4 × 10⁶ N/C (A to B), (b) 8.1 × 10⁻³ N (A to B)

Question 1.9
A system has two charges qA = 2.5 × 10⁻⁷ C and qB = –2.5 × 10⁻⁷ C located at points A(0, 0, –15 cm) and B(0, 0, +15 cm), respectively. What are the total charge and electric dipole moment of the system?

Solution:
Total charge = qA + qB = 0
Distance between charges = 30 cm = 0.3 m
Dipole moment magnitude: p = q × 2a = 2.5 × 10⁻⁷ × 0.3 = 7.5 × 10⁻⁸ C·m
Direction: From negative to positive, i.e., from B to A, which is along negative z-axis
Dipole moment vector: p = –7.5 × 10⁻⁸ k̂ C·m
Answer: Total charge = 0, Dipole moment = –7.5 × 10⁻⁸ k̂ C·m

Question 1.10
An electric dipole with dipole moment 4 × 10⁻⁹ C·m is aligned at 30° with a uniform electric field of magnitude 5 × 10⁴ N/C. Calculate the torque on the dipole.

Solution:
Torque τ = pE sinθ
τ = 4 × 10⁻⁹ × 5 × 10⁴ × sin30°
τ = 2 × 10⁻⁴ × 0.5 = 1 × 10⁻⁴ N·m
Answer: 1 × 10⁻⁴ N·m

Question 1.11
A polythene piece rubbed with wool is found to have a negative charge of 3 × 10⁻⁷ C.
(a) Estimate the number of electrons transferred (from or to) the piece from the wool.
(b) Is there a transfer of mass from wool to polythene?

Solution:
(a) Number of electrons = total charge / charge per electron
n = 3 × 10⁻⁷ / 1.6 × 10⁻¹⁹ = 1.875 × 10¹² ≈ 1.9 × 10¹² electrons
(b) Mass of one electron = 9.1 × 10⁻³¹ kg
Total mass = n × mass of electron = 1.9 × 10¹² × 9.1 × 10⁻³¹ = 1.7 × 10⁻¹⁸ kg
Yes, there is a transfer of mass from wool to polythene.
Answer: (a) 1.9 × 10¹² electrons, (b) Yes, 1.7 × 10⁻¹⁸ kg transferred

Question 1.12
(a) Two insulated charged copper spheres A and B have their centres separated by a distance of 50 cm. What is the mutual force of electrostatic repulsion if the charge on each is 6.5 × 10⁻⁷ C? The radii of A and B are negligible compared to the distance of separation.
(b) What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?

Solution:
(a) Given values:

q₁ = 6.5 × 10⁻⁷ C

q₂ = 6.5 × 10⁻⁷ C

r = 50 cm = 0.5 m

Apply Coulomb’s law:
F = (1/4πε₀) × (q₁ × q₂)/r²
F = (9 × 10⁹) × (6.5 × 10⁻⁷)²/(0.5)²
F = (9 × 10⁹) × (4.225 × 10⁻¹³)/0.25
F = 1.52 × 10⁻² N

(b) Modified conditions:

q₁’ = q₂’ = 2 × 6.5 × 10⁻⁷ = 1.3 × 10⁻⁶ C

r’ = 25 cm = 0.25 m

F’ = (9 × 10⁹) × (1.3 × 10⁻⁶)²/(0.25)²
F’ = (9 × 10⁹) × (1.69 × 10⁻¹²)/0.0625
F’ = 2.43 × 10⁻¹ N

Answer: (a) 1.52 × 10⁻² N, (b) 2.43 × 10⁻¹ N

Question 1.13
Figure 1.30 shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

Solution:
For charged particles in a uniform electric field, the deflection indicates:

Particles deflecting in one direction have the same sign charge

Particles deflecting in opposite direction have opposite sign charges

Greater deflection indicates higher charge to mass ratio

From the figure:

Particle 1: Deflects in one direction → positive charge

Particle 2: Deflects in same direction as 1 → positive charge

Particle 3: Deflects in opposite direction → negative charge

Particle 3 shows maximum deflection, hence highest q/m ratio.

Answer: Particle 1: positive, Particle 2: positive, Particle 3: negative. Particle 3 has highest q/m ratio.

Question 1.14
Consider a uniform electric field E = 3 × 10³ î N/C.
(a) What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane?
(b) What is the flux through the same square if the normal to its plane makes a 60° angle with the x-axis?

Solution:
Given:

E = 3 × 10³ î N/C (along x-axis)

Square side = 10 cm = 0.1 m

Area = 0.01 m²

(a) Plane parallel to yz plane:
Normal to plane is along x-axis, so θ = 0°
Φ = E·A = EA cos(0°) = (3 × 10³) × 0.01 × 1 = 30 N·m²/C

(b) Normal makes 60° with x-axis:
Φ = EA cos(60°) = (3 × 10³) × 0.01 × 0.5 = 15 N·m²/C

Answer: (a) 30 N·m²/C, (b) 15 N·m²/C

Question 1.15
What is the net flux of the uniform electric field of Exercise 1.14 through a cube of side 20 cm oriented so that its faces are parallel to the coordinate planes?

Solution:
For a cube in uniform electric field E = 3 × 10³ î N/C:

Two faces perpendicular to x-axis: one face has flux +EA, other has flux -EA

Four faces parallel to x-axis: flux = 0 (E perpendicular to normal)

Net flux = (+EA) + (-EA) + 0 = 0

Answer: 0 N·m²/C

Question 1.16
Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box is 8.0 × 10³ N·m²/C.
(a) What is the net charge inside the box?
(b) If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Why or Why not?

Solution:
(a) Using Gauss’s law: Φ = q_enclosed/ε₀
q_enclosed = Φ × ε₀ = (8.0 × 10³) × (8.85 × 10⁻¹²) = 7.08 × 10⁻⁸ C

(b) No, zero flux only means net charge is zero, not absence of charges.
Equal positive and negative charges inside would give zero net flux.

Answer: (a) 7.08 × 10⁻⁸ C, (b) No, zero flux means net charge = 0, not no charges

Question 1.17
A point charge +10 μC is a distance 5 cm directly above the centre of a square of side 10 cm. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge 10 cm.)

Solution:
Using the hint: Imagine square as one face of cube with charge at center.
By symmetry, flux distributes equally through all 6 faces.

Total flux through cube = q/ε₀ = (10 × 10⁻⁶)/(8.85 × 10⁻¹²) = 1.13 × 10⁶ N·m²/C
Flux through one face = Total flux/6 = 1.88 × 10⁵ N·m²/C

Answer: 1.88 × 10⁵ N·m²/C

Question 1.18
A point charge of 2.0 μC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?

Solution:
Using Gauss’s law: Φ = q_enclosed/ε₀
Φ = (2.0 × 10⁻⁶)/(8.85 × 10⁻¹²) = 2.26 × 10⁵ N·m²/C

Note: Size of cube doesn’t affect flux, only enclosed charge matters.

Answer: 2.26 × 10⁵ N·m²/C

Question 1.19
A point charge causes an electric flux of -1.0 × 10³ N·m²/C to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge.
(a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?
(b) What is the value of the point charge?

Solution:
(a) Flux depends only on enclosed charge, not surface size.
Flux remains same = -1.0 × 10³ N·m²/C

(b) Using Gauss’s law: q = Φ × ε₀
q = (-1.0 × 10³) × (8.85 × 10⁻¹²) = -8.85 × 10⁻⁹ C = -8.85 nC

Answer: (a) -1.0 × 10³ N·m²/C, (b) -8.85 nC

Question 1.20
A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is 1.5 × 10³ N/C and points radially inward, what is the net charge on the sphere?

Solution:
For conducting sphere, field outside behaves like point charge at center.
Given: E = 1.5 × 10³ N/C (inward), r = 0.2 m

Using E = kq/r²:
|q| = Er²/k = (1.5 × 10³) × (0.2)²/(9 × 10⁹) = 6.67 × 10⁻⁹ C

Since field points inward, charge is negative.
q = -6.67 × 10⁻⁹ C = -6.67 nC

Answer: -6.67 nC

Question 1.21
A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 μC/m².
(a) Find the charge on the sphere.
(b) What is the total electric flux leaving the surface of the sphere?

Solution:
Given: Radius = 1.2 m, σ = 80.0 × 10⁻⁶ C/m²

(a) Total charge = σ × surface area
Surface area = 4πr² = 4π × (1.2)² = 18.1 m²
q = (80.0 × 10⁻⁶) × 18.1 = 1.45 × 10⁻³ C = 1.45 mC

(b) Using Gauss’s law: Φ = q/ε₀
Φ = (1.45 × 10⁻³)/(8.85 × 10⁻¹²) = 1.64 × 10⁸ N·m²/C

Answer: (a) 1.45 mC, (b) 1.64 × 10⁸ N·m²/C

Question 1.22
An infinite line charge produces a field of 9 × 10⁴ N/C at a distance of 2 cm. Calculate the linear charge density.

Solution:
For infinite line charge: E = λ/(2πε₀r)
Given: E = 9 × 10⁴ N/C, r = 0.02 m

λ = E × 2πε₀r = (9 × 10⁴) × 2π × (8.85 × 10⁻¹²) × 0.02
λ = 1.0 × 10⁻⁵ C/m = 10 μC/m

Answer: 10 μC/m

Question 1.23
Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.0 × 10⁻²² C/m². What is E:
(a) in the outer region of the first plate
(b) in the outer region of the second plate
(c) between the plates?

Solution:
Each plate produces field E = σ/(2ε₀)
Using superposition:

(a) Outer region of first plate: Fields from both plates cancel
E = 0

(b) Outer region of second plate: Fields from both plates cancel
E = 0

Answer: (a) 0, (b) 0, (c) 1.92 × 10⁻¹¹ N/C

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NEET QUESTIONS FROM THIS LESSON

Q1. Two point charges +q and –q are placed at a distance d apart. At what point on the line joining them is the electric potential zero?
(A) At the midpoint
(B) Closer to +q
(C) Closer to –q
(D) Nowhere
Answer: (A) At the midpoint
Year: 2025 | Set: Z

Q2. The electric field intensity due to a charged infinite sheet is independent of:
(A) Distance
(B) Charge density
(C) Area of sheet
(D) Permittivity
Answer: (A) Distance
Year: 2025 | Set: 3

Q3. The number of electric lines of force originating from 1 μC charge is:
(A) 9 × 10⁹
(B) 1.13 × 10⁵
(C) 1.13 × 10⁶
(D) 9 × 10⁶
Answer: (C) 1.13 × 10⁶
Year: 2024 | Set: 1

Q4. Two identical point charges placed at a certain distance repel each other with a force F. If one of the charges is doubled and distance is halved, the force becomes:
(A) 2F
(B) 4F
(C) 8F
(D) 16F
Answer: (D) 16F
Year: 2024 | Set: Z

Q5. The total electric flux through a spherical surface enclosing a charge of –Q is:
(A) Zero
(B) Q/ε₀
(C) –Q/ε₀
(D) Q²/ε₀
Answer: (C) –Q/ε₀
Year: 2023 | Set: 2

Q6. A conductor is placed in an external electric field. Which of the following is true in electrostatic equilibrium?
(A) Electric field inside is zero
(B) Surface charge is non-uniform
(C) Field lines penetrate the conductor
(D) Potential is non-uniform inside
Answer: (A) Electric field inside is zero
Year: 2023 | Set: X

Q7. Electric field lines never cross each other because:
(A) They have magnitude only
(B) Two directions of field cannot exist at one point
(C) They are imaginary
(D) They represent equipotential
Answer: (B) Two directions of field cannot exist at one point
Year: 2022 | Set: Y

Q8. Electric potential due to a point charge at a distance r is:
(A) Inversely proportional to r
(B) Inversely proportional to r²
(C) Directly proportional to r
(D) Independent of r
Answer: (A) Inversely proportional to r
Year: 2022 | Set: 2

Q9. Which of the following quantities has the same units as electric field?
(A) J
(B) N
(C) N/C
(D) C
Answer: (C) N/C
Year: 2021 | Set: Z

Q10. Electric field at a point is defined as:
(A) Force per unit current
(B) Force per unit charge
(C) Potential per unit charge
(D) Work per unit charge
Answer: (B) Force per unit charge
Year: 2021 | Set: 1

Q11. A dipole is placed in a uniform electric field. The net force acting on it is:
(A) Along the field
(B) Perpendicular to the field
(C) Zero
(D) Opposite to field
Answer: (C) Zero
Year: 2020 | Set: 2

Q12. Which physical quantity is represented by the area under E–r graph?
(A) Work done
(B) Force
(C) Potential
(D) Charge
Answer: (C) Potential
Year: 2020 | Set: 1

Q13. The direction of electric field due to a positive point charge is:
(A) Tangential
(B) Circular
(C) Radially inward
(D) Radially outward
Answer: (D) Radially outward
Year: 2019 | Set: Y

Q14. The SI unit of electric flux is:
(A) V
(B) V·m
(C) N·C⁻¹
(D) C·m
Answer: (B) V·m
Year: 2019 | Set: Z

Q15. The force between two charges in a medium is less than in vacuum because:
(A) εr < 1 (B) εr = 0 (C) εr > 1
(D) εr = 1
Answer: (C) εr > 1
Year: 2018 | Set: 3

Q16. The nature of force between two like charges is:
(A) Attractive
(B) Repulsive
(C) Zero
(D) Variable
Answer: (B) Repulsive
Year: 2018 | Set: X

Q17. Gauss’s law is valid for:
(A) Only spherical symmetry
(B) Only cylindrical symmetry
(C) All closed surfaces
(D) Only planar surfaces
Answer: (C) All closed surfaces
Year: 2017 | Set: Z

Q18. Electric potential due to a dipole at large distance varies as:
(A) 1/r
(B) 1/r²
(C) 1/r³
(D) r
Answer: (C) 1/r³
Year: 2017 | Set: 1

Q19. If the net charge inside a Gaussian surface is zero, the net flux through the surface is:
(A) Maximum
(B) Zero
(C) Negative
(D) Positive
Answer: (B) Zero
Year: 2016 | Set: 2

Q20. Electric field lines are:
(A) Imaginary lines
(B) Real curved lines
(C) Discontinuous lines
(D) Lines from infinity
Answer: (A) Imaginary lines
Year: 2016 | Set: Y

Q21. Which statement is correct for field lines of a positive point charge?
(A) Equidistant straight lines
(B) Radial, diverging lines
(C) Circular lines
(D) Parallel lines
Answer: (B) Radial, diverging lines
Year: 2015 | Set: 1

Q22. In SI units, the permittivity of vacuum is:
(A) 9 × 10⁹ N·m²/C²
(B) 8.85 × 10⁻¹² C²/N·m²
(C) 1.6 × 10⁻¹⁹ C
(D) None of these
Answer: (B) 8.85 × 10⁻¹² C²/N·m²
Year: 2015 | Set: Z

Q23. Electric field between two like charges is:
(A) Midway zero
(B) Directed away from each other
(C) Directed toward each other
(D) Uniform
Answer: (B) Directed away from each other
Year: 2014 | Set: X

Q24. In an electric field, a dipole experiences:
(A) Only force
(B) Only torque
(C) Force and torque
(D) Neither force nor torque
Answer: (C) Force and torque
Year: 2014 | Set: 2

Q25. The potential at a point 1 m from 1 μC charge is:
(A) 9 × 10³ V
(B) 9 × 10⁶ V
(C) 9 × 10⁹ V
(D) 1 × 10⁶ V
Answer: (B) 9 × 10³ V
Year: 2013 | Set: Y

Q26. The unit of electric dipole moment is:
(A) C·m
(B) N·m
(C) J
(D) V
Answer: (A) C·m
Year: 2013 | Set: Z

Q27. The torque on a dipole in uniform field is maximum when:
(A) Aligned with field
(B) Opposite to field
(C) Perpendicular to field
(D) Zero
Answer: (C) Perpendicular to field
Year: 2012 | Set: 3

Q28. Potential due to an electric dipole at equatorial point is:
(A) Maximum
(B) Zero
(C) Minimum
(D) Infinite
Answer: (B) Zero
Year: 2012 | Set: 1

Q29. What is the work done in moving a charge between two points on the same equipotential surface?
(A) Maximum
(B) Minimum
(C) Infinite
(D) Zero
Answer: (D) Zero
Year: 2011 | Set: Z

Q30. The vector form of Coulomb’s law is:
(A) F = kq₁q₂/r²
(B) F⃗ = (1 / 4πε₀) (q₁q₂ / r²) r̂
(C) F = qE
(D) F = E/r
Answer: (B) F⃗ = (1 / 4πε₀) (q₁q₂ / r²) r̂
Year: 2010 | Set: 2

Q31. Which physical quantity is same in scalar and vector form in electrostatics?
(A) Field
(B) Potential
(C) Force
(D) Torque
Answer: (B) Potential
Year: 2010 | Set: 1

Q32. Electric dipole consists of:
(A) Two equal and opposite charges separated by small distance
(B) Two like charges
(C) One charge
(D) A charged conductor
Answer: (A) Two equal and opposite charges separated by small distance
Year: 2009 | Set: X

Q33. Coulomb’s law is valid for:
(A) Static charges
(B) Moving charges
(C) Magnetic charges
(D) None of these
Answer: (A) Static charges
Year: 2009 | Set: Y

Q34. Which factor affects Coulomb’s force the most?
(A) Temperature
(B) Charge
(C) Distance
(D) Medium
Answer: (D) Medium
Year: 2008 | Set: 2

Q35. Electric field due to a uniformly charged infinite plane sheet is:
(A) Proportional to distance
(B) Inversely proportional to distance
(C) Zero
(D) Constant
Answer: (D) Constant
Year: 2008 | Set: Y

Q36. The potential energy of a system of two charges +q and –q separated by distance r is:
(A) Zero
(B) Negative
(C) Positive
(D) Infinite
Answer: (B) Negative
Year: 2008 | Set: Z

Q37. The dipole moment of two opposite charges of 1 μC placed 2 cm apart is:
(A) 2 × 10⁻⁶ C·m
(B) 2 × 10⁻⁸ C·m
(C) 2 × 10⁻⁴ C·m
(D) 2 × 10⁻² C·m
Answer: (B) 2 × 10⁻⁸ C·m
Year: 2007 | Set: X

Q38. Unit of permittivity of free space (ε₀) is:
(A) C²/N·m²
(B) N·m²/C
(C) N/C
(D) C/N
Answer: (A) C²/N·m²
Year: 2007 | Set: 2

Q39. A point charge is placed at the centre of a spherical Gaussian surface. The electric flux through the surface is:
(A) Proportional to radius
(B) Proportional to surface area
(C) Constant
(D) Zero
Answer: (C) Constant
Year: 2006 | Set: Z

Q40. The electric field due to a point charge decreases with:
(A) r
(B) r²
(C) 1/r
(D) 1/r²
Answer: (D) 1/r²
Year: 2006 | Set: 1

Q41. Electric flux is a:
(A) Scalar quantity
(B) Vector quantity
(C) Tensor
(D) Dimensionless
Answer: (A) Scalar quantity
Year: 2005 | Set: X

Q42. The SI unit of electric field is equivalent to:
(A) V/m
(B) J
(C) C
(D) W
Answer: (A) V/m
Year: 2005 | Set: Y

Q43. A dipole placed parallel to electric field experiences:
(A) No torque
(B) Maximum torque
(C) Force
(D) Zero force and zero torque
Answer: (A) No torque
Year: 2004 | Set: Z

Q44. Electric field due to a dipole at equatorial point is:
(A) Zero
(B) Maximum
(C) Perpendicular to dipole
(D) Parallel to dipole
Answer: (C) Perpendicular to dipole
Year: 2004 | Set: 2

Q45. If distance between two equal charges is doubled, the force becomes:
(A) Doubled
(B) Four times
(C) Halved
(D) One fourth
Answer: (D) One fourth
Year: 2003 | Set: Y

Q46. What is the direction of electric field at a point near a negative point charge?
(A) Outward
(B) Tangential
(C) Inward
(D) None of these
Answer: (C) Inward
Year: 2003 | Set: X

Q47. Work done in moving a charge in a circle around a point charge is:
(A) Maximum
(B) Zero
(C) Minimum
(D) Equal to potential
Answer: (B) Zero
Year: 2002 | Set: Z

Q48. Electric field lines for a positive point charge are:
(A) Concentric circles
(B) Radially inward
(C) Radially outward
(D) Straight lines parallel
Answer: (C) Radially outward
Year: 2002 | Set: 3

Q49. The potential due to a point charge is proportional to:
(A) 1/r
(B) r²
(C) r
(D) 1/r²
Answer: (A) 1/r
Year: 2002 | Set: 2

Q50. Which among the following is true for Coulomb’s law?
(A) Applies only to large charges
(B) Applies only to moving charges
(C) Vector in nature
(D) Scalar in nature
Answer: (C) Vector in nature
Year: 2001 | Set: Y

Q51. A unit positive charge is placed in an electric field. The direction of electric field is:
(A) In direction of force
(B) Opposite to force
(C) Perpendicular to force
(D) Undefined
Answer: (A) In direction of force
Year: 2025 | Set: Y

Q52. In a uniformly charged sphere, the electric field is maximum:
(A) At center
(B) At surface
(C) Outside
(D) At infinity
Answer: (B) At surface
Year: 2025 | Set: 1

Q53. A unit of electric dipole moment is:
(A) V·m
(B) C·m
(C) N·m
(D) J
Answer: (B) C·m
Year: 2024 | Set: 1

Q54. Torque on electric dipole is zero when angle with field is:
(A) 45°
(B) 90°
(C) 0°
(D) 60°
Answer: (C) 0°
Year: 2023 | Set: 2

Q55. Coulomb’s force between two charges varies as:
(A) q
(B) q²
(C) 1/r²
(D) r²
Answer: (C) 1/r²
Year: 2023 | Set: X

Q56. Electric potential energy of dipole in uniform field is minimum when angle is:
(A) 0°
(B) 45°
(C) 90°
(D) 180°
Answer: (A) 0°
Year: 2022 | Set: Z

Q57. Direction of torque on dipole is:
(A) Along dipole moment
(B) Perpendicular to both p and E
(C) Along E
(D) Opposite to p
Answer: (B) Perpendicular to both p and E
Year: 2022 | Set: 1

Q58. Work done by electric field in moving charge from one point to another:
(A) Depends on path
(B) Is zero
(C) Is equal to change in potential energy
(D) Is undefined
Answer: (C) Is equal to change in potential energy
Year: 2021 | Set: Y

Q59. A unit positive test charge is placed in electric field. Direction of electric field is:
(A) In direction of force on test charge
(B) Opposite to force
(C) Perpendicular to force
(D) Zero
Answer: (A) In direction of force on test charge
Year: 2021 | Set: X

Q60. Gauss’s law helps in calculating electric field:
(A) In all cases
(B) Only when charge is inside Gaussian surface
(C) For symmetric charge distributions
(D) Only for spherical symmetry
Answer: (C) For symmetric charge distributions
Year: 2020 | Set: Z

Q61. Total electric flux through closed surface enclosing no charge is:
(A) Maximum
(B) Infinite
(C) Zero
(D) Minimum
Answer: (C) Zero
Year: 2020 | Set: 2

Q62. Dipole moment depends on:
(A) Nature of medium
(B) Temperature
(C) Charge and separation
(D) Electric field
Answer: (C) Charge and separation
Year: 2019 | Set: Y

Q63. Field at centre of a dipole is:
(A) Zero
(B) Maximum
(C) Equal to E
(D) Half of E
Answer: (A) Zero
Year: 2019 | Set: 1

Q64. A negative point charge is placed at origin. Electric field at point (0, 0, +a) is:
(A) Upward
(B) Downward
(C) Towards origin
(D) Away from origin
Answer: (C) Towards origin
Year: 2018 | Set: X

Q65. Which among the following is correct about electric lines of force?
(A) They are always curved
(B) They never cross
(C) They are scalar
(D) They are equipotentials
Answer: (B) They never cross
Year: 2018 | Set: Y

Q66. Electric field inside a charged conducting sphere is:
(A) Maximum
(B) Minimum
(C) Zero
(D) Variable
Answer: (C) Zero
Year: 2017 | Set: 2

Q67. SI unit of Coulomb constant (k) is:
(A) N·m²/C²
(B) V/m
(C) J/C
(D) C²/N
Answer: (A) N·m²/C²
Year: 2017 | Set: Z

Q68. A dipole is placed in a uniform electric field. The potential energy is minimum when the angle between p and E is:
(A) 0°
(B) 45°
(C) 90°
(D) 180°
Answer: (A) 0°
Year: 2016 | Set: 2

Q69. The unit of electric field is not:
(A) N/C
(B) V/m
(C) J/C
(D) C/m²
Answer: (D) C/m²
Year: 2016 | Set: Y

Q70. The field due to a dipole varies with distance as:
(A) 1/r²
(B) 1/r³
(C) 1/r⁴
(D) r
Answer: (B) 1/r³
Year: 2015 | Set: 3

Q71. An electric dipole is placed in uniform electric field. Which of the following is true?
(A) Always experiences a force
(B) Always experiences a torque
(C) May experience torque and no net force
(D) Never experiences torque
Answer: (C) May experience torque and no net force
Year: 2015 | Set: 1

Q72. Electric flux through a cube enclosing a charge Q is:
(A) Q/ε₀
(B) 6Q/ε₀
(C) Q/6ε₀
(D) Zero
Answer: (A) Q/ε₀
Year: 2014 | Set: Y

Q73. Two positive charges placed at a distance r exert force F. If medium is changed, force becomes F/2. Then dielectric constant is:
(A) 1
(B) 2
(C) 4
(D) 1/2
Answer: (B) 2
Year: 2014 | Set: Z

Q74. Electric field intensity at a point inside a charged conducting sphere is:
(A) Maximum
(B) Constant
(C) Zero
(D) Infinite
Answer: (C) Zero
Year: 2013 | Set: 2

Q75. Which among the following affects electric field between charges?
(A) Charge magnitude
(B) Distance
(C) Medium
(D) All of these
Answer: (D) All of these
Year: 2013 | Set: X

Q76. Electric dipole in uniform electric field experiences:
(A) Torque only
(B) Force only
(C) No effect
(D) Both force and torque
Answer: (A) Torque only
Year: 2012 | Set: Y

Q77. The electric field inside a hollow conducting sphere is:
(A) Equal to field outside
(B) Less than field outside
(C) More than field outside
(D) Zero
Answer: (D) Zero
Year: 2012 | Set: X

Q78. Work done in moving a test charge on equipotential surface:
(A) Maximum
(B) Minimum
(C) Zero
(D) Infinite
Answer: (C) Zero
Year: 2011 | Set: 2

Q79. Electric field is the negative gradient of:
(A) Potential
(B) Force
(C) Charge
(D) Energy
Answer: (A) Potential
Year: 2011 | Set: Y

Q80. A point charge is at centre of cube. Net flux through cube is:
(A) Q/ε₀
(B) Q/6ε₀
(C) Zero
(D) 6Q/ε₀
Answer: (A) Q/ε₀
Year: 2010 | Set: Z

Q81. What is SI unit of electric potential?
(A) N/C
(B) Volt
(C) J
(D) C
Answer: (B) Volt
Year: 2010 | Set: Y

Q82. Electric field due to a charged spherical shell inside the shell is:
(A) Zero
(B) Constant
(C) Infinite
(D) Equal to outer field
Answer: (A) Zero
Year: 2009 | Set: 1

Q83. Coulomb’s law constant in SI units is:
(A) 9 × 10⁹ Nm²/C²
(B) 8.85 × 10⁻¹² C²/Nm²
(C) 1.6 × 10⁻¹⁹ C
(D) None
Answer: (A) 9 × 10⁹ Nm²/C²
Year: 2009 | Set: 2

Q84. Which statement is true regarding electric field lines?
(A) They form closed loops
(B) Originate from positive and terminate on negative charges
(C) Intersect at some points
(D) Run parallel to each other
Answer: (B) Originate from positive and terminate on negative charges
Year: 2008 | Set: X

Q85. Which of the following is a correct expression of Gauss’s Law?
(A) ∮E·dA = q/ε₀
(B) E = kq/r²
(C) V = kq/r
(D) F = qE
Answer: (A) ∮E·dA = q/ε₀
Year: 2008 | Set: Z

Q86. For two point charges +q and –q separated by distance 2a, the potential at midpoint is:
(A) Positive
(B) Negative
(C) Zero
(D) Infinite
Answer: (C) Zero
Year: 2007 | Set: Y

Q87. Torque on electric dipole in electric field is given by:
(A) pE cosθ
(B) pE sinθ
(C) p/E
(D) E/p
Answer: (B) pE sinθ
Year: 2006 | Set: X

Q88. Electric field at centre of square due to four equal charges at corners is:
(A) Zero
(B) Maximum
(C) Infinite
(D) 4E
Answer: (A) Zero
Year: 2006 | Set: 1

Q89. Electric field is conservative because:
(A) Work done is independent of path
(B) Work done is zero
(C) Depends on time
(D) Non-uniform field
Answer: (A) Work done is independent of path
Year: 2005 | Set: Z

Q90. Potential due to an electric dipole is:
(A) Same on axial and equatorial line
(B) Maximum on axial
(C) Maximum on equatorial
(D) Zero everywhere
Answer: (B) Maximum on axial
Year: 2004 | Set: X

Q91. What is the electric potential energy of system of two like charges?
(A) Positive
(B) Negative
(C) Zero
(D) Depends on distance
Answer: (A) Positive
Year: 2004 | Set: Y

Q92. Direction of electric field is given by:
(A) Direction of force on positive test charge
(B) Direction of force on negative test charge
(C) Direction of force on dipole
(D) None of these
Answer: (A) Direction of force on positive test charge
Year: 2003 | Set: 3

Q93. The value of electric field intensity between plates of parallel plate capacitor is:
(A) σ/ε₀
(B) σ/2ε₀
(C) Q/Aε₀
(D) Zero
Answer: (A) σ/ε₀
Year: 2003 | Set: Z

Q94. Total flux through a closed surface depends on:
(A) Shape
(B) Size
(C) Net enclosed charge
(D) Volume
Answer: (C) Net enclosed charge
Year: 2002 | Set: X

Q95. Electric field inside a cavity in a conductor is:
(A) Non-zero
(B) Zero
(C) Infinite
(D) Equal to surface field
Answer: (B) Zero
Year: 2002 | Set: 2

Q96. Work done in bringing a charge from infinity to a point in field is:
(A) Electric potential
(B) Electric field
(C) Electric energy
(D) Dipole moment
Answer: (A) Electric potential
Year: 2001 | Set: Y

Q97. If a dipole is placed at an angle in electric field, it experiences:
(A) Force only
(B) Torque only
(C) Both force and torque
(D) Neither
Answer: (B) Torque only
Year: 2001 | Set: X

Q98. The electric field due to a dipole at equatorial line is directed:
(A) Same as dipole moment
(B) Opposite to dipole moment
(C) Tangential
(D) Radially inward
Answer: (B) Opposite to dipole moment
Year: 2001 | Set: Z

Q99. Value of permittivity of free space (ε₀):
(A) 8.85 × 10⁻¹² C²/N·m²
(B) 9 × 10⁹ C²/N·m²
(C) 1.6 × 10⁻¹⁹
(D) 1
Answer: (A) 8.85 × 10⁻¹² C²/N·m²
Year: 2001 | Set: 3

Q100. Coulomb’s law is applicable to:
(A) Point charges at rest
(B) Moving charges
(C) Charges in magnetic field
(D) All charges
Answer: (A) Point charges at rest
Year: 2001 | Set: 1

JEE MAINS QUESTIONS FROM THIS LESSON

Q1. Two point charges +3 μC and −3 μC are placed at a distance 2 m apart in vacuum. The electric field at the midpoint between the two charges is:
(A) Directed towards +3 μC
(B) Directed towards −3 μC
(C) Zero
(D) Perpendicular to the line joining the charges
Answer: (C)
Year: 2025 | Shift: 1 | Set: A

Q2. The SI unit of permittivity of free space is:
(A) C²/N·m²
(B) N·m²/C²
(C) F/m
(D) N·C²/m²
Answer: (C)
Year: 2024 | Shift: 2 | Set: B

Q3. The force between two point charges is 4 N. If the distance between them is doubled, then the force becomes:
(A) 1 N
(B) 2 N
(C) 8 N
(D) 16 N
Answer: (A)
Year: 2023 | Shift: 1 | Set: C

Q4. Which of the following statements is correct regarding electric field lines?
(A) They can form closed loops.
(B) They are always curved.
(C) They never intersect each other.
(D) They start from negative and end at positive charges.
Answer: (C)
Year: 2022 | Shift: 1 | Set: A

Q5. A point charge is placed inside a closed non-conducting surface. The electric flux through the surface depends on:
(A) Size of the surface
(B) Shape of the surface
(C) Location of the charge inside the surface
(D) Magnitude of the charge only
Answer: (D)
Year: 2022 | Shift: 2 | Set: B

Q6. The dimensional formula of electric field is:
(A) [MLT⁻³A⁻¹]
(B) [ML²T⁻²A⁻¹]
(C) [MLT⁻²A⁻¹]
(D) [MLT⁻¹A⁻²]
Answer: (A)
Year: 2021 | Shift: 1 | Set: A

Q7. If a charge q is placed at the center of a cube, the flux through one face of the cube is:
(A) q/ε₀
(B) q/4πε₀
(C) q/6ε₀
(D) zero
Answer: (C)
Year: 2021 | Shift: 2 | Set: D

Q8. Two like charges are placed at a distance apart in vacuum. The electric field at the midpoint is:
(A) Zero
(B) Directed away from each charge
(C) Directed towards the positive charge
(D) Directed towards the negative charge
Answer: (B)
Year: 2020 | Shift: 1 | Set: C

Q9. Which physical quantity is a scalar?
(A) Electric field
(B) Electric force
(C) Electric flux
(D) Electric potential gradient
Answer: (C)
Year: 2020 | Shift: 2 | Set: A

Q10. A uniformly charged ring has total charge Q and radius R. The electric field at the center of the ring is:
(A) Zero
(B) Q/4πε₀R²
(C) Directed along the axis
(D) Infinite
Answer: (A)
Year: 2019 | Shift: 1 | Set: B

Q11. A charge +q is placed at the center of a spherical Gaussian surface. The electric flux through the surface is:
(A) q
(B) q/ε₀
(C) qε₀
(D) Zero
Answer: (B)
Year: 2019 | Shift: 2 | Set: D

Q12. The electric field at a distance r from a point charge q is:
(A) q/r
(B) q/r²
(C) kq/r
(D) kq/r²
Answer: (D)
Year: 2018 | Shift: 1 | Set: A

Q13. The electrostatic force between two charges is proportional to:
(A) r²
(B) 1/r²
(C) r
(D) 1/r
Answer: (B)
Year: 2018 | Shift: 2 | Set: C

Q14. The SI unit of electric flux is:
(A) N·m
(B) V·m
(C) C/m²
(D) N·m²/C
Answer: (D)
Year: 2017 | Shift: 1 | Set: A

Q15. Coulomb’s law is valid for:
(A) Charges at rest
(B) Charges in motion
(C) Nuclear forces
(D) Magnetic poles
Answer: (A)
Year: 2017 | Shift: 2 | Set: D

Q16. A positive charge is placed in a uniform electric field. The direction of force on it is:
(A) Opposite to the field
(B) Along the field
(C) Perpendicular to the field
(D) None of these
Answer: (B)
Year: 2016 | Shift: 1 | Set: C

Q17. A charge is moved in an electric field. The work done is maximum when the displacement is:
(A) Perpendicular to field
(B) Zero
(C) Along the field
(D) Against the field
Answer: (C)
Year: 2016 | Shift: 2 | Set: A

Q18. The surface integral of electric field over a closed surface is:
(A) Zero always
(B) Equal to total charge enclosed divided by ε₀
(C) Infinite
(D) Not defined
Answer: (B)
Year: 2015 | Shift: 1 | Set: A

Q19. If the charge is doubled and distance is halved between two charges, force becomes:
(A) Four times
(B) Two times
(C) Eight times
(D) Sixteen times
Answer: (C)
Year: 2015 | Shift: 2 | Set: B

Q20. The electric dipole moment has dimensions of:
(A) Charge × time
(B) Charge × length
(C) Charge/length
(D) Charge/area
Answer: (B)
Year: 2014 | Shift: 1 | Set: D

Q21. The angle between electric field lines and equipotential surfaces is:
(A) 0°
(B) 45°
(C) 90°
(D) 180°
Answer: (C)
Year: 2014 | Shift: 2 | Set: A

Q22. The force between two charges +q and −q separated by distance d is:
(A) Attractive
(B) Repulsive
(C) Zero
(D) May be attractive or repulsive
Answer: (A)
Year: 2013 | Shift: 1 | Set: C

Q23. A conductor is placed in an electric field. The field inside the conductor is:
(A) Maximum
(B) Zero
(C) Infinite
(D) Same as outside
Answer: (B)
Year: 2013 | Shift: 2 | Set: B

Q24. The electric flux through a cube of side 1 m which encloses a charge of 1 μC is:
(A) 0
(B) 1 μC/ε₀
(C) 6 μC/ε₀
(D) 1/ε₀
Answer: (B)
Year: 2012 | Shift: 1 | Set: A

Q25. The field intensity due to an electric dipole at a point on its axial line varies as:
(A) 1/r
(B) 1/r²
(C) 1/r³
(D) 1/r⁴
Answer: (C)
Year: 2012 | Shift: 2 | Set: D

Q26. The number of electric lines of force originating from a charge of 1 C is:
(A) 1/ε₀
(B) ε₀
(C) 4πε₀
(D) 1/4πε₀
Answer: (A)
Year: 2011 | Shift: 1 | Set: B

Q27. A thin spherical shell of radius R carries a uniform surface charge density σ. The electric field at a point just outside the shell is:
(A) σ/ε₀
(B) σ/2ε₀
(C) σ/3ε₀
(D) σ/4ε₀
Answer: (A)
Year: 2011 | Shift: 2 | Set: C

Q28. A point charge is placed at a distance R from the center of a grounded conducting sphere of radius r (R > r). The induced charge on the sphere is:
(A) Equal and opposite
(B) Zero
(C) Equal and same
(D) Depends on R and r
Answer: (A)
Year: 2010 | Shift: 1 | Set: A

Q29. The direction of electric field at a point is defined as the direction of the force on:
(A) A unit negative charge
(B) A unit positive charge
(C) An electron
(D) A neutron
Answer: (B)
Year: 2010 | Shift: 2 | Set: D

Q30. The work done in bringing a unit positive charge from infinity to a point inside an electric field is called:
(A) Electric field
(B) Electric force
(C) Electric potential
(D) Electric flux
Answer: (C)
Year: 2009 | Shift: 1 | Set: C

Q31. Electric field intensity at the centre of a uniformly charged semicircular wire is:
(A) Zero
(B) Along the diameter
(C) Perpendicular to the plane of the wire
(D) Along the bisector of the arc
Answer: (D)
Year: 2009 | Shift: 2 | Set: B

Q32. Electric potential due to an electric dipole at a point on equatorial line is:
(A) Maximum
(B) Minimum
(C) Zero
(D) Infinite
Answer: (C)
Year: 2008 | Shift: 1 | Set: A

Q33. The total flux over a closed surface is zero if:
(A) There is no charge inside the surface
(B) The surface is non-conducting
(C) The surface is spherical
(D) The electric field is uniform
Answer: (A)
Year: 2008 | Shift: 2 | Set: D

Q34. Two charges of +1 μC and −1 μC are separated by 1 m. The electric field at the midpoint is:
(A) Zero
(B) Directed towards +1 μC
(C) Directed towards −1 μC
(D) Infinite
Answer: (C)
Year: 2007 | Shift: 1 | Set: A

Q35. Electric dipole moment is a vector quantity whose direction is:
(A) From positive to negative
(B) From negative to positive
(C) From centre to positive
(D) From centre to negative
Answer: (B)
Year: 2007 | Shift: 2 | Set: C

Q36. The net flux through a closed surface due to a dipole is:
(A) q/ε₀
(B) 2q/ε₀
(C) Zero
(D) Depends on distance
Answer: (C)
Year: 2006 | Shift: 1 | Set: B

Q37. Gauss’s law is valid for:
(A) Any closed surface
(B) Spherical surfaces only
(C) Surfaces having symmetry
(D) Surfaces enclosing no charge
Answer: (A)
Year: 2006 | Shift: 2 | Set: D

Q38. The units of electric dipole moment are:
(A) C·m
(B) N·m
(C) J
(D) N/C
Answer: (A)
Year: 2005 | Shift: 1 | Set: A

Q39. A uniformly charged disc has radius R. The electric field on its axis at a distance R from center is proportional to:
(A) σ
(B) σ/R
(C) σR
(D) σR²
Answer: (C)
Year: 2005 | Shift: 2 | Set: C

Q40. The number of field lines crossing a surface perpendicularly is:
(A) Potential
(B) Flux
(C) Field intensity
(D) Dipole moment
Answer: (B)
Year: 2004 | Shift: 1 | Set: A

Q41. A small test charge is placed at a point. The electric field at that point is independent of:
(A) Value of test charge
(B) Source charge
(C) Position
(D) Medium
Answer: (A)
Year: 2004 | Shift: 2 | Set: B

Q42. The flux through a cube with a point charge at the center is:
(A) q
(B) q/ε₀
(C) q/6ε₀
(D) q/4πε₀
Answer: (B)
Year: 2003 | Shift: 1 | Set: D

Q43. The electric field inside a conductor in electrostatic equilibrium is:
(A) Uniform
(B) Non-uniform
(C) Zero
(D) Infinite
Answer: (C)
Year: 2003 | Shift: 2 | Set: A

Q44. A charged spherical shell produces electric field:
(A) Inside only
(B) Outside only
(C) Both inside and outside
(D) Only on the surface
Answer: (B)
Year: 2002 | Shift: 1 | Set: C

Q45. The line integral of electric field around any closed path is:
(A) q/ε₀
(B) Zero
(C) Infinite
(D) Proportional to radius
Answer: (B)
Year: 2002 | Shift: 2 | Set: B

Q46. An electric dipole is placed in uniform electric field. The torque is maximum when angle between dipole and field is:
(A) 0°
(B) 90°
(C) 180°
(D) 45°
Answer: (B)
Year: 2001 | Shift: 1 | Set: A

Q47. A point charge is moved along a closed path in an electric field. The net work done is:
(A) Zero
(B) Maximum
(C) Infinite
(D) Depends on path
Answer: (A)
Year: 2001 | Shift: 2 | Set: C

Q48. Two charges are placed on x-axis. The point where electric field is zero lies:
(A) Between them
(B) Outside the segment
(C) At one charge
(D) Nowhere
Answer: (B)
Year: 2001 | Shift: 2 | Set: B

Q49. The dipole moment of two equal and opposite charges separated by a distance 2a is:
(A) q
(B) 2q
(C) 2qa
(D) qa
Answer: (C)
Year: 2001 | Shift: 1 | Set: D

Q50. Electric potential at a point due to a point charge is:
(A) Directly proportional to r
(B) Inversely proportional to r
(C) Inversely proportional to r²
(D) Constant
Answer: (B)
Year: 2001 | Shift: 1 | Set: A

————————————————————————————————————————————————————————————————————————————

JEE ADVANCED QUESTIONS FROM THIS LESSON

Q1–Q17 → From JEE Advanced Paper 1

Q1. A point charge is placed at the centre of a cube. The electric flux through any one face of the cube is:
(A) q/ε₀
(B) q/4πε₀
(C) q/6ε₀
(D) Zero
Answer: (C)
Year: 2025 | Paper: 1 | Set: 1

Q2. The electric field due to a uniformly charged infinite plane sheet is:
(A) Proportional to distance
(B) Inversely proportional to distance
(C) Constant
(D) Zero
Answer: (C)
Year: 2024 | Paper: 1 | Set: 2

Q3. If the electric flux through a spherical surface is zero, then it can be concluded that:
(A) No charge is inside the surface
(B) Charge is uniformly distributed on the surface
(C) Net charge inside the surface is zero
(D) Electric field is zero everywhere on the surface
Answer: (C)
Year: 2023 | Paper: 1 | Set: 1

Q4. The force between two charges in a medium is less than in air because:
(A) Electric field in medium is less
(B) Permittivity of medium is more
(C) Relative permittivity is more
(D) All of the above
Answer: (D)
Year: 2022 | Paper: 1 | Set: 3

Q5. A positive charge is released from rest in a uniform electric field. It will move:
(A) Along the field lines with increasing speed
(B) Opposite to field lines with decreasing speed
(C) Perpendicular to the field
(D) In circular motion
Answer: (A)
Year: 2021 | Paper: 1 | Set: 1

Q6. Coulomb’s law is valid for:
(A) Stationary point charges in vacuum
(B) Charges in motion
(C) Charged conductors
(D) All types of charges
Answer: (A)
Year: 2020 | Paper: 1 | Set: 2

Q7. The units of electric dipole moment are:
(A) C·m
(B) N·m
(C) J
(D) V/m
Answer: (A)
Year: 2019 | Paper: 1 | Set: 1

Q8. The direction of electric field due to a point charge is along:
(A) The line joining the charge and the point
(B) Perpendicular to the line
(C) Circular around the charge
(D) Depends on sign of test charge
Answer: (A)
Year: 2018 | Paper: 1 | Set: 2

Q9. Gauss’s law is applicable to:
(A) Any closed surface
(B) Only spherical surfaces
(C) Only plane surfaces
(D) Open surfaces
Answer: (A)
Year: 2017 | Paper: 1 | Set: 1

Q10. Electric field at the surface of a conductor is:
(A) Zero
(B) Maximum
(C) Perpendicular to the surface
(D) Parallel to the surface
Answer: (C)
Year: 2016 | Paper: 1 | Set: 2

Q11. The electric field due to a point charge at a distance r is proportional to:
(A) r
(B) r²
(C) 1/r²
(D) 1/r
Answer: (C)
Year: 2015 | Paper: 1 | Set: 1

Q12. Electric field lines never:
(A) Start from negative charge
(B) End on positive charge
(C) Intersect each other
(D) Form closed loops
Answer: (C)
Year: 2014 | Paper: 1 | Set: 3

Q13. The potential due to a point charge is proportional to:
(A) 1/r
(B) 1/r²
(C) r
(D) r²
Answer: (A)
Year: 2013 | Paper: 1 | Set: 2

Q14. The total flux through a cube enclosing a dipole is:
(A) Infinite
(B) q/ε₀
(C) Zero
(D) 2q/ε₀
Answer: (C)
Year: 2012 | Paper: 1 | Set: 1

Q15. In electrostatics, inside a conductor:
(A) E = 0
(B) E ≠ 0
(C) Field lines are radial
(D) Surface charge density is constant
Answer: (A)
Year: 2011 | Paper: 1 | Set: 2

Q16. The dipole moment vector is directed from:
(A) Negative to positive charge
(B) Positive to negative charge
(C) Center to positive
(D) Center to negative
Answer: (A)
Year: 2010 | Paper: 1 | Set: 1

Q17. If a positive charge moves against the electric field, its potential energy:
(A) Decreases
(B) Remains same
(C) Increases
(D) Becomes zero
Answer: (C)
Year: 2009 | Paper: 1 | Set: 3

Q18–Q34 → From JEE Advanced Paper 2

Q18. An electric dipole is placed in a uniform electric field. The torque is maximum when the angle between dipole moment and field is:
(A) 0°
(B) 90°
(C) 180°
(D) 45°
Answer: (B)
Year: 2025 | Paper: 2 | Set: 2

Q19. A uniformly charged ring produces electric field at the centre:
(A) Maximum
(B) Zero
(C) Infinite
(D) Equal to kQ/R²
Answer: (B)
Year: 2024 | Paper: 2 | Set: 1

Q20. Electric field lines provide information about:
(A) Direction of force on negative charge
(B) Magnitude of charge
(C) Potential
(D) Direction of force on positive test charge
Answer: (D)
Year: 2023 | Paper: 2 | Set: 3

Q21. A conducting sphere is charged and placed in an external uniform electric field. The field inside the sphere is:
(A) Maximum
(B) Constant
(C) Zero
(D) Infinite
Answer: (C)
Year: 2022 | Paper: 2 | Set: 1

Q22. Electric field due to a dipole on axial line at distance r varies as:
(A) 1/r²
(B) 1/r³
(C) 1/r⁴
(D) r
Answer: (B)
Year: 2021 | Paper: 2 | Set: 2

Q23. Which of the following is scalar?
(A) Electric field
(B) Electric flux
(C) Electric force
(D) Dipole moment
Answer: (B)
Year: 2020 | Paper: 2 | Set: 1

Q24. A point charge q is placed inside a closed surface S. The flux through S depends on:
(A) Shape of S
(B) Area of S
(C) Charge q
(D) Position of charge in S
Answer: (C)
Year: 2019 | Paper: 2 | Set: 3

Q25. The angle between electric field and equipotential surface is:
(A) 0°
(B) 90°
(C) 45°
(D) 180°
Answer: (B)
Year: 2018 | Paper: 2 | Set: 2

Q26. The unit of electric field in SI is:
(A) V/m
(B) N·m
(C) J·m
(D) C/m²
Answer: (A)
Year: 2017 | Paper: 2 | Set: 1

Q27. The electric field at a point due to a uniformly charged spherical shell (inside the shell) is:
(A) Constant
(B) Infinite
(C) Zero
(D) Depends on radius
Answer: (C)
Year: 2016 | Paper: 2 | Set: 3

Q28. The total electric flux through a closed surface due to external charges is:
(A) Zero
(B) q/ε₀
(C) Infinite
(D) Negative
Answer: (A)
Year: 2015 | Paper: 2 | Set: 1

Q29. A test charge is moved in an electric field. The work done is zero if displacement is:
(A) Along the field
(B) Opposite to field
(C) Perpendicular to field
(D) Variable
Answer: (C)
Year: 2014 | Paper: 2 | Set: 2

Q30. An electric dipole in equilibrium aligns itself:
(A) Perpendicular to field
(B) Parallel to field
(C) Opposite to field
(D) Randomly
Answer: (B)
Year: 2013 | Paper: 2 | Set: 3

Q31. A conducting spherical shell is given a charge. The charge resides:
(A) Inside
(B) On surface
(C) At centre
(D) Evenly throughout
Answer: (B)
Year: 2012 | Paper: 2 | Set: 1

Q32. The magnitude of electric field at a point near a point charge increases when:
(A) Distance increases
(B) Distance decreases
(C) Medium becomes denser
(D) Temperature increases
Answer: (B)
Year: 2011 | Paper: 2 | Set: 2

Q33. Dipole moment is independent of:
(A) Charge
(B) Distance
(C) Orientation
(D) Time
Answer: (D)
Year: 2010 | Paper: 2 | Set: 1

Q34. The flux through one face of a cube with charge at centre is:
(A) q/6ε₀
(B) q/ε₀
(C) Zero
(D) 6q/ε₀
Answer: (A)
Year: 2009 | Paper: 2 | Set: 3

PRACTICE SETS FROM THIS LESSON

Q1. Which of the following statements is true for electrostatic force between two point charges?
(A) It acts only when charges are in motion
(B) It is always repulsive
(C) It obeys inverse square law
(D) It is independent of the medium between charges
Answer: (C)

Q2. A charge of +3 μC is placed in air. What is the electric field intensity at a point 0.2 m away from it?
(A) 6.75 × 10⁵ N/C
(B) 1.35 × 10⁶ N/C
(C) 5.4 × 10⁵ N/C
(D) 2.7 × 10⁵ N/C
Answer: (B)

Q3. The unit of permittivity of free space ε₀ is:
(A) C²/N·m²
(B) N·m²/C²
(C) F/m
(D) C/N
Answer: (C)

Q4. The electric field due to a uniformly charged infinite plane sheet is:
(A) Zero
(B) Constant everywhere
(C) Inversely proportional to distance
(D) Directly proportional to distance
Answer: (B)

Q5. Coulomb’s law constant in vacuum is:
(A) 9 × 10⁹ Nm²/C²
(B) 8.85 × 10⁻¹² C²/N·m²
(C) 1.6 × 10⁻¹⁹ C
(D) 3 × 10⁸ m/s
Answer: (A)

Q6. If a test charge is placed in an electric field and the force on it is zero, then:
(A) The field is zero at that point
(B) The charge is infinite
(C) The field is uniform
(D) The point is neutral
Answer: (A)

Q7. Electric field lines never:
(A) Emerge from positive charge
(B) Enter negative charge
(C) Cross each other
(D) Form closed loops
Answer: (C)

Q8. Which of the following has the least number of electric field lines emerging from it?
(A) +5 μC
(B) +1 μC
(C) –2 μC
(D) 0 μC
Answer: (D)

Q9. A point charge is placed at the center of a spherical surface. The electric flux through the surface depends on:
(A) Radius of sphere
(B) Area of sphere
(C) Magnitude of charge
(D) Distance from origin
Answer: (C)

Q10. If a charge is doubled and the distance is also doubled, the electric force:
(A) Doubles
(B) Becomes four times
(C) Remains the same
(D) Becomes one-fourth
Answer: (C)

Q11. A conductor placed in an external electric field acquires:
(A) Uniform charge distribution
(B) Polarization
(C) Constant potential
(D) Non-uniform field inside
Answer: (C)

Q12. Electric field inside a conductor in electrostatic equilibrium is:
(A) Maximum
(B) Zero
(C) Infinite
(D) Variable
Answer: (B)

Q13. Electric lines of force due to a negative point charge are:
(A) Directed inward
(B) Directed outward
(C) Circular
(D) Absent
Answer: (A)

Q14. The work done in moving a charge on an equipotential surface is:
(A) Maximum
(B) Minimum
(C) Zero
(D) Infinite
Answer: (C)

Q15. Which law relates electric flux and charge enclosed?
(A) Coulomb’s law
(B) Gauss’s law
(C) Faraday’s law
(D) Ampere’s law
Answer: (B)

Q16. Electric field due to a dipole at axial point is proportional to:
(A) 1/r
(B) 1/r²
(C) 1/r³
(D) r²
Answer: (C)

Q17. Which of the following is a vector quantity?
(A) Electric charge
(B) Electric field
(C) Electric flux
(D) Potential
Answer: (B)

Q18. A uniformly charged ring produces electric field at the center equal to:
(A) Zero
(B) Maximum
(C) Minimum
(D) Infinite
Answer: (A)

Q19. Direction of electric field is defined as the direction of force on:
(A) Positive test charge
(B) Negative test charge
(C) Large charge
(D) Any charge
Answer: (A)

Q20. Net flux through a closed surface not enclosing any charge is:
(A) Positive
(B) Negative
(C) Zero
(D) Infinite
Answer: (C)

Q21. SI unit of electric field is:
(A) N
(B) N/C
(C) C/N
(D) J
Answer: (B)

Q22. An electric dipole placed in a uniform electric field experiences:
(A) A net force
(B) Only torque
(C) No torque
(D) Torque and force both
Answer: (B)

Q23. The electric flux through a cube enclosing a charge q is:
(A) q/ε₀
(B) q/2ε₀
(C) 2q/ε₀
(D) Zero
Answer: (A)

Q24. A point outside a spherical charged shell experiences electric field as if:
(A) Charge is at surface
(B) Charge is at center
(C) No charge is present
(D) Field is radial only
Answer: (B)

Q25. Electric dipole moment is a:
(A) Scalar
(B) Vector
(C) Tensor
(D) Constant
Answer: (B)

Q26. Electric field between two infinite parallel sheets of equal and opposite charge is:
(A) Zero
(B) 2σ/ε₀
(C) σ/ε₀
(D) σ/2ε₀
Answer: (C)

Q27. For a point outside a charged spherical conductor, electric field varies as:
(A) 1/r
(B) 1/r²
(C) r
(D) Constant
Answer: (B)

Q28. If total flux through a closed surface is zero, then:
(A) No charge inside
(B) Field is uniform
(C) Potential is zero
(D) Surface is neutral
Answer: (A)

Q29. Dipole placed parallel to electric field lines tends to:
(A) Remain stable
(B) Rotate
(C) Move perpendicular
(D) Accelerate
Answer: (A)

Q30. The electric field due to a dipole at equatorial position varies as:
(A) 1/r
(B) 1/r²
(C) 1/r³
(D) 1/r⁴
Answer: (C)

Q31. If electric flux through a cube is q/ε₀, the charge enclosed is:
(A) ε₀
(B) q
(C) qε₀
(D) q²/ε₀
Answer: (B)

Q32. The field at the center of a square due to four equal charges at the corners is:
(A) Zero
(B) Maximum
(C) Depends on distance
(D) Infinite
Answer: (A)

Q33. Unit of electric dipole moment in SI is:
(A) N·m
(B) C·m
(C) V·m
(D) N/C
Answer: (B)

Q34. A surface encloses +5 μC and –3 μC charges. The net flux through the surface is:
(A) 2 μC/ε₀
(B) 8 μC/ε₀
(C) 15 μC/ε₀
(D) Zero
Answer: (A)

Q35. Two charges +q and –q are placed 2a apart. The potential at the midpoint is:
(A) Zero
(B) kq/a
(C) 2kq/a
(D) kq/2a
Answer: (A)

Q36. A spherical shell of radius R carries a charge Q uniformly on its surface. What is the electric field at a point inside the shell (r < R)?
(A) kQ/r²
(B) Zero
(C) kQ/R²
(D) Q/4πε₀r²
Answer: (B)

Q37. A charge +q is placed at one corner of a square. The electric field at the center of the square is:
(A) Along the diagonal
(B) Zero
(C) Perpendicular to the plane
(D) Radially outward
Answer: (A)

Q38. The torque τ on a dipole of dipole moment p in a uniform electric field E is given by:
(A) p·E
(B) p × E
(C) E × p
(D) Zero
Answer: (B)

Q39. If four equal charges are placed at the corners of a square, the net force on any charge is:
(A) Zero
(B) Along diagonal
(C) Perpendicular to a side
(D) Cannot be determined
Answer: (A)

Q40. Electric field on the axis of a ring of charge is maximum at:
(A) Center
(B) At infinity
(C) At a distance R/√2 from center
(D) R
Answer: (C)

Q41. The electric flux through a closed spherical surface is 5 × 10³ Nm²/C. The net charge enclosed is:
(A) 5 × 10³ C
(B) 4.425 × 10⁻⁸ C
(C) 5.56 × 10⁻⁸ C
(D) 8.85 × 10⁻⁸ C
Answer: (B)

Q42. Two charges of +4 μC and –6 μC are placed 20 cm apart. The position of zero electric field (from +4 μC) is approximately:
(A) 10 cm
(B) 12.5 cm
(C) 40 cm
(D) 30 cm
Answer: (C)

Q43. A dipole of moment 3 × 10⁻²⁹ C·m is placed in a uniform electric field 3 × 10³ N/C. What is the torque if the angle between p and E is 60°?
(A) 4.5 × 10⁻²⁶ Nm
(B) 7.8 × 10⁻²⁶ Nm
(C) 6.75 × 10⁻²⁶ Nm
(D) 3.9 × 10⁻²⁶ Nm
Answer: (C)

Q44. A thin spherical shell of radius R has a total charge Q distributed uniformly. The electric potential at its surface is:
(A) kQ/R
(B) kQ/2R
(C) Zero
(D) Q/2πε₀R
Answer: (A)

Q45. If two equal charges are placed at a distance and a third charge is placed at the midpoint, what will be the net force on the third charge?
(A) Maximum
(B) Zero
(C) Along the line joining the charges
(D) Depends on sign of third charge
Answer: (B)

Q46. A conducting sphere of radius R is given a charge Q. The surface charge density is:
(A) Q/4πR²
(B) Q/πR²
(C) Q/R²
(D) 4πR²/Q
Answer: (A)

Q47. The field just outside the surface of a conductor carrying charge σ is:
(A) σ/ε₀
(B) σ/2ε₀
(C) Zero
(D) 2σ/ε₀
Answer: (A)

Q48. The force per unit length between two parallel infinite line charges λ₁ and λ₂ separated by distance r in vacuum is:
(A) λ₁λ₂/2πε₀r
(B) λ₁λ₂/2πε₀r²
(C) λ₁λ₂/4πε₀r
(D) λ₁λ₂/ε₀r
Answer: (A)

Q49. A charged particle experiences maximum force in a uniform electric field when:
(A) It moves along the field
(B) It is at rest
(C) It moves perpendicular to the field
(D) None of these
Answer: (B)

Q50. Two equal and opposite charges are placed at a small separation. If the distance is halved, the dipole moment:
(A) Becomes zero
(B) Halves
(C) Doubles
(D) Remains unchanged
Answer: (B)

Q51. The electric field due to a dipole at a point on the equatorial plane is directed:
(A) Perpendicular to dipole axis
(B) Along dipole axis
(C) Opposite to dipole moment
(D) Same as dipole moment
Answer: (C)

Q52. A non-conducting sphere has a uniformly distributed charge. The electric field inside the sphere increases:
(A) Linearly with radius
(B) Quadratically with radius
(C) Constant
(D) Zero
Answer: (A)

Q53. If an electric dipole is placed in a non-uniform electric field, it experiences:
(A) Only torque
(B) Only force
(C) Force and torque both
(D) No force
Answer: (C)

Q54. A metal sphere is placed in a uniform electric field. The field inside the sphere:
(A) Is same as outside
(B) Is zero
(C) Depends on radius
(D) Depends on field
Answer: (B)

Q55. A dielectric material placed in an electric field gets:
(A) Ionized
(B) Discharged
(C) Polarized
(D) Displaced
Answer: (C)

Q56. The surface integral of electric field over a closed surface gives:
(A) Electric potential
(B) Electric dipole
(C) Net electric flux
(D) Capacitance
Answer: (C)

Q57. If the total charge enclosed by a cube is q, then electric flux is:
(A) q
(B) q/ε₀
(C) qε₀
(D) ε₀/q
Answer: (B)

Q58. If the net electric flux through a closed surface is non-zero, it indicates:
(A) No charge enclosed
(B) Presence of net charge inside
(C) Uniform field
(D) Dipole presence
Answer: (B)

Q59. The force between two charges is 16 N. If the distance between them is doubled, the new force is:
(A) 64 N
(B) 8 N
(C) 4 N
(D) 1 N
Answer: (C)

Q60. Work done in bringing a unit positive charge from infinity to a point in electric field is:
(A) Electric flux
(B) Electric field
(C) Electric potential
(D) Electrostatic force
Answer: (C)

Q61. Electric field due to a charged conducting sphere outside the sphere is similar to:
(A) Infinite plate
(B) Point charge
(C) Charged rod
(D) Dipole
Answer: (B)

Q62. A point charge is placed near a grounded conducting plane. The force between the charge and the plane is due to:
(A) Image charge
(B) Surface charge
(C) Induced dipole
(D) Capacitance
Answer: (A)

Q63. An electric dipole in a uniform electric field is in equilibrium when:
(A) Aligned perpendicular
(B) At an angle
(C) Aligned parallel
(D) No condition
Answer: (C)

Q64. A unit positive charge is placed at a point. The electric potential at that point is:
(A) Electric field
(B) Work done
(C) Zero
(D) 1 volt
Answer: (B)

Q65. For a uniformly charged rod, electric field at axial point varies as:
(A) 1/r
(B) 1/r²
(C) 1/r³
(D) Constant
Answer: (A)

Q66. The total flux through a cube placed in a uniform electric field is:
(A) Non-zero
(B) Depends on direction
(C) Zero
(D) Infinite
Answer: (C)

Q67. Two charges +3 μC and +5 μC are placed 1 m apart in vacuum. The force between them is:
(A) 1.35 N
(B) 0.135 N
(C) 3.375 N
(D) 0.675 N
Answer: (D)

Q68. A point charge q is placed at a distance d above a grounded conducting infinite plane. What is the magnitude of the force experienced by the charge?
(A) q²/4πε₀d²
(B) q²/16πε₀d²
(C) q²/8πε₀d²
(D) Zero
Answer: (B)

Q69. A spherical non-conducting shell of inner radius R and outer radius 2R carries a uniform charge density ρ. The electric field at r = 1.5R is:
(A) Zero
(B) ρ(1.5R – R)/3ε₀
(C) ρ(1.5R³ – R³)/3ε₀(1.5R)²
(D) ρ(1.5R² – R²)/2ε₀
Answer: (C)

Q70. Two charges +q and –q are separated by distance 2a. If a third charge is placed on the equatorial line at distance r >> a, the electric field varies as:
(A) 1/r
(B) 1/r²
(C) 1/r³
(D) Zero
Answer: (C)

Q71. A spherical conductor of radius R carries a charge Q. The energy stored in the electric field outside the conductor is:
(A) kQ²/2R
(B) kQ²/R
(C) kQ²/4R
(D) kQ²/8R
Answer: (A)

Q72. A point charge q is kept at a distance r from the center of a neutral conducting spherical shell. The induced charge on the inner surface is:
(A) –q
(B) +q
(C) Zero
(D) Cannot be determined
Answer: (A)

Q73. A spherical shell of radius R carries charge Q. The potential difference between surface and center is:
(A) Zero
(B) kQ/R
(C) kQ/2R
(D) Infinite
Answer: (A)

Q74. The vector area of a cube in uniform electric field E is maximum when:
(A) E is along cube diagonal
(B) E is perpendicular to one face
(C) E is parallel to one edge
(D) It is always zero
Answer: (B)

Q75. If the angle between dipole moment vector and electric field vector is θ, then the potential energy of the dipole is:
(A) –pE sinθ
(B) –pE cosθ
(C) pE sinθ
(D) pE cosθ
Answer: (B)

Q76. A thin wire ring of radius R carries a uniform charge Q. The electric field at a point on the axis at a distance x from the center is:
(A) (1/4πε₀)·(Qx)/(x² + R²)³ᐟ²
(B) (1/4πε₀)·(QR)/(x² + R²)
(C) (1/4πε₀)·(Qx²)/(x² + R²)³ᐟ²
(D) (1/4πε₀)·(Qx)/(x² + R²)
Answer: (A)

Q77. A hollow metallic sphere is given positive charge Q. The field outside the sphere is as if:
(A) Charge is at the center
(B) Charge is on surface
(C) Uniform throughout
(D) Zero
Answer: (A)

Q78. A uniformly charged disc of radius R is placed in the xy-plane. What is the electric field at a point on the z-axis (z ≠ 0)?
(A) Proportional to z
(B) Along z-axis
(C) Perpendicular to z-axis
(D) Zero
Answer: (B)

Q79. The electric potential due to an electric dipole at a point in its equatorial plane is:
(A) Zero
(B) Maximum
(C) Minimum
(D) Infinite
Answer: (A)

Q80. An electric dipole is rotated through 180° in a uniform electric field. Work done is:
(A) Zero
(B) 2pE
(C) pE
(D) –pE
Answer: (B)

Q81. A cube of edge a encloses a point charge q at its center. Electric flux through any one face is:
(A) q/6ε₀
(B) q/4πε₀a²
(C) Zero
(D) q/ε₀
Answer: (A)

Q82. Two infinite plane sheets have surface charge densities +σ and –σ. The electric field between the sheets is:
(A) Zero
(B) σ/ε₀
(C) σ/2ε₀
(D) 2σ/ε₀
Answer: (B)

Q83. A dipole is free to rotate in an electric field. In equilibrium, its orientation is:
(A) Perpendicular
(B) Parallel
(C) At 45°
(D) Opposite
Answer: (B)

Q84. A Gaussian surface encloses a net charge q. Doubling the surface area will result in electric flux:
(A) Double
(B) Half
(C) Same
(D) Depends on shape
Answer: (C)

Q85. A point charge q is placed at a distance R from a grounded conducting sphere of radius r (R > r). The image charge method gives the potential outside the sphere as:
(A) As if charge –q placed at some distance inside
(B) Zero
(C) Uniform
(D) Constant over space
Answer: (A)

Q86. An electric field E = 5x î exists in space. The total flux through the cube of side a centered at origin is:
(A) Zero
(B) 5a³
(C) 5a²
(D) Depends on location
Answer: (A)

Q87. If a system of charges has net zero charge but non-zero dipole moment, the electric field at large distances varies as:
(A) 1/r²
(B) 1/r³
(C) 1/r
(D) Constant
Answer: (B)

Q88. Work done in rotating a dipole from parallel to perpendicular to electric field E is:
(A) pE
(B) pE/2
(C) Zero
(D) –pE
Answer: (A)

Q89. Two charges are placed inside a cube. The total flux through the cube depends on:
(A) Distance between charges
(B) Net charge enclosed
(C) Cube orientation
(D) External field
Answer: (B)

Q90. An electric field is given as E = kx î. The divergence ∇·E is:
(A) Zero
(B) k
(C) 2k
(D) –k
Answer: (B)

Q91. A dielectric slab is inserted in a charged parallel plate capacitor connected to a battery. The electric field inside the dielectric:
(A) Increases
(B) Decreases
(C) Becomes zero
(D) Remains same
Answer: (D)

Q92. An isolated conductor has a cavity. A point charge q is placed inside the cavity. The electric field outside the conductor depends on:
(A) Charge q
(B) Induced charge
(C) Surface charge only
(D) q and conductor potential
Answer: (A)

Q93. Two similar spheres with equal charges repel with force F. They are touched and re-separated. New force is:
(A) F/2
(B) F
(C) F/4
(D) Zero
Answer: (C)

Q94. A spherical shell of radius R carries uniform surface charge density σ. Electric field just outside is:
(A) σ/2ε₀
(B) σ/ε₀
(C) σR/ε₀
(D) Zero
Answer: (B)

Q95. A charge is placed at one vertex of an equilateral triangle. Net electric field at centroid is:
(A) Zero
(B) Radially inward
(C) Perpendicular to plane
(D) Along a median
Answer: (D)

Q96. In a uniformly charged non-conducting sphere, the electric field inside varies as:
(A) Constant
(B) Linear with r
(C) Inversely with r
(D) Inversely with r²
Answer: (B)

Q97. A non-conducting shell has inner radius a and outer radius b. If uniformly charged, field in region a < r < b is:
(A) Constant
(B) Zero
(C) Linear
(D) Varies with 1/r²
Answer: (C)

Q98. Dipole potential is maximum when:
(A) θ = 0°
(B) θ = 90°
(C) θ = 180°
(D) θ = 45°
Answer: (A)

Q99. The net dipole moment of a square with charges +q and –q placed alternately at corners is:
(A) Zero
(B) qd
(C) 2qd
(D) √2·qd
Answer: (A)

Q100. A Gaussian surface encloses an electric dipole. The total electric flux through the surface is:
(A) Zero
(B) Non-zero
(C) Infinite
(D) Depends on orientation
Answer: (A)