Class 12 : Physics (English) – Chapter 2: Electrostatic Potential and Capacitance

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On June 25, 2025

EXPLANATION & SUMMARY

Introduction
Electrostatics is the study of electric charges at rest. In the previous chapter, we learned about electric charges and electric fields. In this chapter, we extend our understanding to electrostatic potential, the concept of potential energy, and the behavior of conductors in an electric field. We also explore capacitance, a measure of how much charge a system can store, and how capacitors work.

Electrostatic Potential
The electrostatic potential at a point in space is defined as the work done per unit positive test charge to bring it from infinity to that point, without any acceleration.
Mathematically:
V = W/q₀
Where:
V is the electrostatic potential
W is the work done in bringing the charge
q₀ is the test charge
It is a scalar quantity and its SI unit is volt (V).

Potential Due to a Point Charge
Let a charge q be located at a point in space. The potential at a distance r from the charge is:
V = (1/4πε₀) × (q/r)
This shows that the potential decreases with distance and is directly proportional to the magnitude of the charge.

Potential Due to an Electric Dipole
An electric dipole consists of two equal and opposite charges separated by a small distance. The potential at a point P at a distance r from the center of the dipole, making an angle θ with the axis, is:
V = (1/4πε₀) × (p cosθ / r²)
Where p = q × 2a is the dipole moment.

Potential Due to a System of Charges
If multiple charges q₁, q₂, q₃,… are present, the potential at a point due to all of them is:
V = V₁ + V₂ + V₃ + … = Σ (1/4πε₀) × (qᵢ / rᵢ)
Since potential is a scalar quantity, we add algebraically.

Equipotential Surfaces
Equipotential surfaces are those where the potential is constant everywhere. No work is done in moving a test charge on an equipotential surface.
Key Properties:
Electric field lines are perpendicular to equipotential surfaces.
For a point charge, equipotential surfaces are spherical in shape.
The closer the surfaces, the stronger the electric field.

Relationship Between Electric Field and Potential
The electric field is related to the rate of change of potential with distance:
E = -dV/dr
In vector form:
𝐄 = -∇V
This negative sign indicates that electric field points in the direction of decreasing potential.

Electrostatic Potential Energy
It is the work done in assembling a system of charges. For two point charges q₁ and q₂ separated by a distance r:
U = (1/4πε₀) × (q₁q₂ / r)
For a system of three or more charges, we calculate the energy for each pair and sum them.

Potential Energy in an External Field
A single charge q in an external field E has potential energy:
U = qV
A dipole in a uniform electric field has potential energy:
U = -p · E = -pE cosθ
Where θ is the angle between the dipole moment vector p and the electric field E.

Conductors in Electrostatic Equilibrium
Important Properties:
Electric field inside a conductor is zero.
Potential is constant throughout the conductor and on its surface.
Electric field just outside a conductor is perpendicular to its surface.
Charge resides only on the outer surface of a conductor.

Capacitance
Capacitance is the ability of a conductor to store charge.
Defined as:
C = q/V
Where:
C is the capacitance
q is the charge stored
V is the potential difference
SI Unit: Farad (F)
1 F = 1 C/V

Capacitance of an Isolated Spherical Conductor
For a spherical conductor of radius R:
C = 4πε₀R
It shows that capacitance is directly proportional to the radius of the sphere.

Parallel Plate Capacitor
Two large conducting plates separated by a small distance d, area A, facing each other, form a capacitor.
Capacitance:
C = ε₀A/d
This is the most basic capacitor design.

Capacitor with Dielectric
A dielectric is a non-conducting material inserted between the plates of a capacitor. It increases the capacitance by reducing the effective electric field.
New capacitance:
C = Kε₀A/d
Where:
K is the dielectric constant (>1)
The dielectric increases capacitance K times.

Series and Parallel Combination of Capacitors
Series Combination:
1/C = 1/C₁ + 1/C₂ + 1/C₃ + …
Total voltage divides, same charge on each.
Parallel Combination:
C = C₁ + C₂ + C₃ + …
Voltage same across all, charge divides.

Energy Stored in a Capacitor
When a capacitor is charged, it stores energy in the form of electrostatic potential energy.
Stored energy:
U = ½ CV²
Other forms:
U = ½ qV = q² / (2C)
This energy is stored in the electric field between the plates.

Energy Density of Electric Field
Energy stored per unit volume between the plates:
u = ½ ε₀E²
Where E is the electric field.

Van de Graaff Generator
This is a high-voltage electrostatic generator based on the principle of charging by conduction.
Working principle:
A moving belt transfers charge to a hollow metallic sphere.
Charges accumulate on the outer surface, achieving high potential.
Used in particle accelerators and nuclear experiments.

✍ SUMMARY (Approx. 300 Words)
Electrostatic potential (V) is the work done per unit positive test charge to bring it from infinity to a point in an electric field.
V = (1/4πε₀) × (q/r) for a point charge.
Electric dipole produces potential:
V = (1/4πε₀) × (p cosθ / r²)
Equipotential surfaces are surfaces with constant potential and are perpendicular to electric field lines.

The electric field is the negative gradient of the potential:
E = -dV/dr
Electrostatic potential energy is the work required to assemble a system of charges. For two charges:
U = (1/4πε₀)(q₁q₂/r)
A conductor in electrostatic equilibrium has zero electric field inside and constant potential throughout.

Capacitance (C) is the ability to store charge per unit voltage:
C = q/V
Capacitance of:
Isolated sphere: C = 4πε₀R
Parallel plates: C = ε₀A/d
With dielectric: C = Kε₀A/d

In series, capacitors share same charge; voltage adds:
1/C = 1/C₁ + 1/C₂ + …
In parallel, capacitors share same voltage; charge adds:
C = C₁ + C₂ + …
Energy stored: U = ½ CV²
Energy density: u = ½ ε₀E²
Van de Graaff generator is a device to generate very high voltages using a moving belt and a metallic dome.

This chapter bridges electric field concepts with potential energy and introduces storage elements like capacitors, essential in circuits and electrostatic devices.

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QUESTIONS FROM TEXTBOOK

Q 2.1: Zero Potential Points
Question: Two charges +5×10⁻⁸ C and –3×10⁻⁸ C are 0.16 m apart. Locate the point(s) on the line joining them where the electric potential is zero.
Answer and Discussion:
Let the +5×10⁻⁸ C charge be at x = 0 and the –3×10⁻⁸ C charge at x = 0.16 m. Let the point where potential is zero be at a distance r from the +5×10⁻⁸ C charge.
Total potential at that point:
V = k [5×10⁻⁸ / r – 3×10⁻⁸ / (0.16 – r)] = 0
Solving:
(5×10⁻⁸)/r = (3×10⁻⁸)/(0.16 – r)
5(0.16 – r) = 3r
0.8 – 5r = 3r
0.8 = 8r → r = 0.10 m or 10 cm
Another case: Point beyond the –3×10⁻⁸ C charge (r > 0.16 m)
5/(r) = 3/(r – 0.16)
5(r – 0.16) = 3r → 5r – 0.8 = 3r → 2r = 0.8 → r = 0.4 m or 40 cm
Thus, the points where potential is zero are at 10 cm and 40 cm from the +5×10⁻⁸ C charge.
Extended Concept: At these points, the algebraic sum of potentials due to both charges cancels out. Unlike electric field (a vector), potential is scalar and adds algebraically. Therefore, two points exist for opposite charges where the potential is zero—one between them and one outside.

Q 2.2: Potential at Center of Hexagon
Question: A regular hexagon has charges of +5 μC at each vertex. Side of hexagon is 10 cm. Find the potential at the center.
Answer and Discussion:
Distance from center to any vertex = side = 0.10 m
Total potential at center:
V = 6 × kq / r = 6 × (9×10⁹) × (5×10⁻⁶) / 0.10
= 6 × 45×10³ = 270×10³ V = 2.7×10⁵ V
Extended Concept: All six vertices contribute equally due to symmetry. Electric potential, being a scalar, adds up simply. This demonstrates the superposition principle for potential and shows how symmetry simplifies calculations.

Q 2.3: Equipotential Surface for a Dipole
Question: Two charges +2 μC and –2 μC are 6 cm apart.
(a) Identify an equipotential surface.
(b) What is the direction of the electric field at that surface?
Answer and Discussion:
(a) The perpendicular bisector of the dipole is an equipotential surface since every point on it is equidistant from both charges. The net potential at any point on this bisector is zero.
(b) The electric field is always perpendicular to equipotential surfaces and points from the positive charge to the negative charge.
Extended Concept: Equipotential surfaces are always perpendicular to electric field lines. In the case of a dipole, the mid-plane is at zero potential and forms an important basis for understanding molecular dipoles and electrostatic shielding.

Q 2.4: Electric Field Around Spherical Conductor
Question: A spherical conductor of radius 12 cm carries charge 1.6×10⁻⁷ C. Find electric field:
(a) Inside the sphere
(b) Just outside the surface
(c) At 18 cm from the center
Answer and Discussion:
(a) Inside a conductor: E = 0
(b) Outside surface (r = 0.12 m):
E = kQ / r² = (9×10⁹ × 1.6×10⁻⁷) / (0.12)²
= 1.0×10⁵ N/C
(c) At 18 cm = 0.18 m:
E = (9×10⁹ × 1.6×10⁻⁷) / (0.18)² = 4.4×10⁴ N/C
Extended Concept: This follows from Gauss’s Law. Inside a conductor, charges rearrange such that the net electric field is zero. Outside, the field behaves as if the entire charge is concentrated at the center.

Q 2.5: Capacitance with Dielectric and Plate Distance Change
Question: A parallel-plate capacitor has air and capacitance 8 pF. Distance is halved, and dielectric of k = 6 inserted. Find new capacitance.
Answer and Discussion:
Original: C ∝ 1/d
New: C’ = k × (C × 2) = 2kC = 2×6×8 = 96 pF
Extended Concept: Capacitance increases due to both decreased plate separation and the dielectric. Dielectrics reduce effective electric field, allowing more charge storage for the same voltage.

Q 2.6: Capacitors in Series
Question: Three capacitors of 9 pF each in series.
(a) Find equivalent capacitance
(b) Find voltage across each when connected to 120 V
Answer and Discussion:
(a) 1/Ceq = 1/9 + 1/9 + 1/9 = 3/9 → Ceq = 3 pF
(b) Q = Ceq × V = 3×10⁻¹² × 120 = 3.6×10⁻¹⁰ C
V across each: V = Q/C = 3.6×10⁻¹⁰ / 9×10⁻¹² = 40 V
Extended Concept: In series, charge is constant across capacitors. Voltage divides in inverse ratio to capacitance. This principle is used in high-voltage circuits where multiple capacitors share potential.

Q 2.7: Capacitors in Parallel
Question: Capacitors 2 pF, 3 pF, 4 pF in parallel.
(a) Find equivalent capacitance
(b) Find individual charges with 100 V supply
Answer and Discussion:
(a) Ceq = 2 + 3 + 4 = 9 pF
(b)
Q₁ = 2×10⁻¹² × 100 = 2.0×10⁻¹⁰ C
Q₂ = 3×10⁻¹² × 100 = 3.0×10⁻¹⁰ C
Q₃ = 4×10⁻¹² × 100 = 4.0×10⁻¹⁰ C
Extended Concept: Voltage remains constant across parallel branches, and total charge is the sum of individual charges. This configuration is ideal for increasing overall capacitance.

Q 2.8: Design of Parallel Plate Capacitor
Question: Plates of area 6×10⁻³ m², separated by 3 mm.
(a) Find capacitance
(b) Charge with 100 V supply
Answer and Discussion:
(a) C = ε₀A/d = (8.854×10⁻¹² × 6×10⁻³) / (3×10⁻³)
= 17.7 pF
(b) Q = CV = 17.7×10⁻¹² × 100 = 1.77×10⁻⁹ C
Extended Concept: Capacitance increases with plate area and decreases with separation. This is the working principle behind most commercial capacitors.

Q 2.9: Dielectric Insertion in Capacitor
Question: A 3 mm mica slab (k = 6) is inserted into the capacitor of Q2.8.
(a) With supply connected
(b) With supply disconnected
Answer and Discussion:
C’ = kC = 6 × 17.7 = 106 pF
(a) Supply connected (V = constant):
Q’ = C’V = 106×10⁻¹² × 100 = 1.06×10⁻⁸ C
E remains the same
(b) Supply disconnected (Q = constant):
V’ = Q / C’ = 1.77×10⁻⁹ / 106×10⁻¹² = 16.7 V
Extended Concept: With connected supply, charge increases. With disconnected supply, voltage decreases. The work done appears as mechanical energy or internal heating.

Q 2.10: Energy Stored in a Capacitor
Question: Capacitor of 12 pF connected to 50 V. Find energy stored.
Answer and Discussion:
U = ½ CV² = ½ × 12×10⁻¹² × (50)² = 1.5×10⁻⁸ J
Extended Concept: This energy is the work done in charging. It’s stored in the electric field and used in devices requiring sudden energy discharge like flashes and defibrillators.

Q 2.11: Energy Loss in Capacitor Sharing
Question: A 600 pF capacitor charged to 200 V is connected to an uncharged identical capacitor. Find energy lost.
Answer and Discussion:
Initial energy:
U₁ = ½ × 600×10⁻¹² × (200)² = 1.2×10⁻⁵ J
Total charge: Q = 600×10⁻¹² × 200 = 1.2×10⁻⁷ C
Final voltage: V = Q / (600 + 600)pF = 100 V
Final energy:
U₂ = ½ × 1200×10⁻¹² × (100)² = 6.0×10⁻⁶ J
Energy lost = U₁ – U₂ = 6.0×10⁻⁶ J
Extended Concept: Half the energy is always lost as heat due to redistribution current in the connecting wires. This is important in practical capacitor applications where loss minimization is needed.

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NEET QUESTIONS FROM THIS LESSON

Section D: Q29–Q31 (4 marks each – Case-based questions)

Q29. Case Study: A parallel plate capacitor is connected across a battery. After charging, the battery is disconnected and a dielectric of constant K is inserted between the plates.
Answer the following:
(a) What happens to the capacitance?
(b) What happens to the potential difference?
(c) What happens to the stored energy?
(d) Justify the change in energy.
Answer:
(a) Capacitance increases (C → KC)
(b) Voltage decreases (V → V/K)
(c) Energy decreases (U → U/K)
(d) Since battery is disconnected, charge remains constant. The insertion of dielectric increases capacitance, so potential drops, and energy (U = Q²/2C) also drops.

Q30. Case Study: An electric dipole consists of charges +q and –q separated by distance 2a. It is placed in a uniform electric field E.
Answer the following:
(a) What is the torque acting on the dipole?
(b) When is the torque maximum?
(c) What is the potential energy of dipole in the field?
(d) When is this potential energy minimum?
Answer:
(a) τ = pE sinθ
(b) Torque is maximum when θ = 90°, i.e., dipole is perpendicular to the field.
(c) U = –pE cosθ
(d) Minimum when θ = 0°, i.e., dipole aligned with field.

Q31. Case Study: A spherical conductor of radius R is charged to a potential V.
Answer the following:
(a) What is the electric field on its surface?
(b) What is the electric field inside the conductor?
(c) What is the potential at the center?
(d) How does potential vary with distance outside the sphere?
Answer:
(a) E = V/R
(b) E = 0 (electric field inside conductor is zero)
(c) V (same as surface, constant throughout)
(d) V(r) = kQ/r ⇒ varies inversely with distance r (like point charge)

Section E: Q32–Q35 (5 marks each – Long answer questions)

Q32. Derive an expression for the capacitance of a parallel plate capacitor. Explain how the capacitance changes with insertion of a dielectric slab.
Answer:
Let area of plates = A, separation = d.
Electric field between plates: E = σ/ε₀ = Q/(Aε₀)
Potential difference: V = Ed = Qd/(Aε₀)
Capacitance: C = Q/V = Aε₀/d
C = ε₀A/d
If dielectric (K) is inserted:
C’ = Kε₀A/d = KC
Hence, capacitance increases K times.

Q33. Three capacitors of 2 μF, 3 μF, and 6 μF are connected in (a) series, (b) parallel. Calculate the equivalent capacitance in both cases. Also find energy stored when connected across 12 V in both arrangements.
Answer:
(a) Series:
1/C = 1/2 + 1/3 + 1/6 = (3+2+1)/6 = 6/6 = 1 ⇒ C_s = 1 μF
U = ½ × 1×10⁻⁶ × (12)² = 72 μJ
(b) Parallel:
C_p = 2 + 3 + 6 = 11 μF
U = ½ × 11×10⁻⁶ × (12)² = 792 μJ

Q34. A capacitor of capacitance 20 μF is connected to a 220 V battery.
(a) Calculate the charge stored and energy stored.
(b) If this capacitor is disconnected and connected to another uncharged 20 μF capacitor, what will be the final voltage and energy lost?
Answer:
(a)
Q = CV = 20×10⁻⁶ × 220 = 4.4 × 10⁻³ C
U = ½ CV² = ½ × 20×10⁻⁶ × (220)² = 0.484 J
(b)
Total capacitance = 40 μF
Final V = Q / C = 4.4 × 10⁻³ / 40×10⁻⁶ = 110 V
Final U = ½ × 40×10⁻⁶ × (110)² = 0.242 J
Energy lost = 0.484 – 0.242 = 0.242 J

Q35. Derive an expression for the electrostatic potential energy stored in a system of two point charges q₁ and q₂ separated by a distance r in vacuum. Also discuss the nature of potential energy for like and unlike charges.
Answer:
Work done in bringing q₂ from infinity to distance r from q₁:
V₁ = kq₁/r
U = q₂V₁ = kq₁q₂/r
Thus,
U = (1/4πε₀) × (q₁q₂ / r)
If q₁ and q₂ are like charges, U is positive (repulsion).
If unlike charges, U is negative (attraction).

Q35. A dielectric material of dielectric constant K is inserted between plates of a capacitor. The new capacitance becomes:
(A) C/K
(B) KC
(C) C + K
(D) CK²
Answer: (B)
Year: 2013 | Set: Q

Q36. Capacitance of a parallel plate capacitor with area A and separation d in vacuum is:
(A) A/d
(B) ε₀A/d
(C) ε₀/dA
(D) Aε₀d
Answer: (B)
Year: 2013 | Set: M

Q37. A 5 µF capacitor is connected to 12 V battery. Energy stored is:
(A) 0.36 mJ
(B) 0.72 mJ
(C) 1.2 mJ
(D) 2.5 mJ
Answer: (B)
Year: 2012 | Set: X

Q38. Two capacitors C₁ and C₂ are connected in series. The equivalent capacitance is:
(A) C₁ + C₂
(B) 1/(1/C₁ + 1/C₂)
(C) C₁C₂/(C₁ + C₂)
(D) Both (B) and (C)
Answer: (D)
Year: 2012 | Set: Z

Q39. The electric field is zero inside a conductor because:
(A) Electrons are stationary
(B) Charges lie on the surface
(C) Field lines cancel inside
(D) Potential is infinite
Answer: (B)
Year: 2012 | Set: P

Q40. A capacitor discharges through a resistor. Potential decreases:
(A) Exponentially
(B) Linearly
(C) Quadratically
(D) Not at all
Answer: (A)
Year: 2011 | Set: Z

Q41. Potential energy of a system of two charges q₁ and q₂ separated by distance r is:
(A) kq₁q₂/r²
(B) kq₁q₂/r
(C) kq₁/q₂
(D) q₁ + q₂
Answer: (B)
Year: 2011 | Set: X

Q42. Energy stored in capacitor is in the form of:
(A) Electric field
(B) Magnetic field
(C) Charge
(D) Kinetic energy
Answer: (A)
Year: 2011 | Set: M

Q43. A point charge is placed at center of conducting shell. Electric field inside shell:
(A) Zero
(B) Infinite
(C) kq/r
(D) Constant
Answer: (A)
Year: 2010 | Set: Y

Q44. Dimensions of capacitance are:
(A) M⁻¹L⁻²T⁴A²
(B) ML²T⁻²
(C) MLT⁻²
(D) MLT
Answer: (A)
Year: 2010 | Set: S1

Q45. When a dielectric slab is inserted in capacitor connected to a battery:
(A) Charge increases
(B) Voltage decreases
(C) Energy increases
(D) Capacitance decreases
Answer: (A)
Year: 2010 | Set: Q

Q46. A capacitor is connected across a battery. If the plates are pulled apart, the energy:
(A) Increases
(B) Decreases
(C) Remains same
(D) Doubles
Answer: (A)
Year: 2009 | Set: X

Q47. Capacitance of system increases when:
(A) Plates are brought closer
(B) Plates are moved apart
(C) Voltage is increased
(D) Current is passed
Answer: (A)
Year: 2009 | Set: Z

Q48. What is the potential energy of a dipole in uniform electric field E making angle θ?
(A) pE sinθ
(B) pE cosθ
(C) -pE cosθ
(D) -pE sinθ
Answer: (C)
Year: 2008 | Set: P

Q49. A capacitor is charged to 50 V. Energy stored is 2.5 mJ. Capacitance is:
(A) 1 µF
(B) 2 µF
(C) 4 µF
(D) 0.5 µF
Answer: (A)
Year: 2008 | Set: Y

Q50. When a dielectric is inserted in an isolated capacitor, what happens to electric field?
(A) Increases
(B) Decreases
(C) Remains same
(D) Becomes zero
Answer: (B)
Year: 2007 | Set: X

Q51. Potential at a point at a distance r due to dipole of moment p is:
(A) p/r
(B) p/r²
(C) p cosθ/4πε₀r²
(D) p sinθ/4πε₀r³
Answer: (C)
Year: 2007 | Set: M

Q52. Which of the following has highest capacitance?
(A) Large area, small distance
(B) Small area, large distance
(C) Small area, small distance
(D) Large area, large distance
Answer: (A)
Year: 2007 | Set: Z

Q53. Electric field is the negative gradient of:
(A) Electric flux
(B) Electric potential
(C) Magnetic flux
(D) Potential energy
Answer: (B)
Year: 2006 | Set: Q

Q54. The capacitance of a parallel plate capacitor is doubled by:
(A) Doubling area
(B) Halving distance
(C) Both
(D) Doubling voltage
Answer: (C)
Year: 2006 | Set: P

Q55. When a dielectric slab is inserted into a charged capacitor:
(A) Energy increases
(B) Potential increases
(C) Energy decreases
(D) Capacitance decreases
Answer: (C)
Year: 2006 | Set: Z

Q56. Electric potential is a:
(A) Vector quantity
(B) Scalar quantity
(C) Tensor
(D) Pseudovector
Answer: (B)
Year: 2005 | Set: Y

Q57. A 4 µF capacitor is charged to 10 V. Energy stored is:
(A) 0.1 mJ
(B) 0.2 mJ
(C) 0.4 mJ
(D) 0.5 mJ
Answer: (C)
Year: 2005 | Set: S2

Q58. Which quantity is same in series combination of capacitors?
(A) Voltage
(B) Capacitance
(C) Charge
(D) Energy
Answer: (C)
Year: 2005 | Set: Q

Q59. In a parallel combination of capacitors:
(A) Voltage is same
(B) Charge is same
(C) Energy is same
(D) Capacitance is same
Answer: (A)
Year: 2004 | Set: M

Q60. A capacitor is connected to a battery and then disconnected. On inserting dielectric:
(A) Charge increases
(B) Voltage decreases
(C) Electric field increases
(D) Voltage decreases
Answer: (B)
Year: 2004 | Set: P

Q61. The SI unit of permittivity is:
(A) F/m
(B) C/V
(C) V/m
(D) C/m²
Answer: (A)
Year: 2004 | Set: Y

Q62. Energy stored in a 2 µF capacitor charged to 50 V is:
(A) 1.25 mJ
(B) 2.5 mJ
(C) 0.5 mJ
(D) 0.25 mJ
Answer: (A)
Year: 2003 | Set: S

Q63. Capacitance does not depend on:
(A) Area
(B) Distance
(C) Medium
(D) Voltage
Answer: (D)
Year: 2003 | Set: X

Q64. Work done in assembling unit charge against potential V is:
(A) V
(B) 1/V
(C) 0
(D) V²
Answer: (A)
Year: 2003 | Set: M

Q65. Unit of electric flux is:
(A) N·m²/C
(B) C·m²/N
(C) V·m
(D) C
Answer: (A)
Year: 2002 | Set: Y

Q66. Dielectric increases capacitance because:
(A) Increases distance
(B) Increases charge
(C) Reduces electric field
(D) All of these
Answer: (C)
Year: 2002 | Set: Z

Q67. A dipole is placed perpendicular to electric field. Torque is:
(A) Maximum
(B) Zero
(C) Minimum
(D) Infinity
Answer: (A)
Year: 2001 | Set: X

Q68. A capacitor stores energy E. If the potential difference is doubled, energy becomes:
(A) 2E
(B) E
(C) 4E
(D) E/2
Answer: (C)
Year: 2001 | Set: Q

Q69. Capacitance of a spherical conductor is directly proportional to:
(A) Square of radius
(B) Inverse of radius
(C) Radius
(D) Area
Answer: (C)
Year: 2001 | Set: M

Q70. Potential due to electric dipole at axial point is proportional to:
(A) 1/r
(B) 1/r²
(C) 1/r³
(D) r
Answer: (C)
Year: 2001 | Set: P

Q71. Capacitance of a cylindrical capacitor depends on:
(A) Area
(B) Radius and length
(C) Voltage
(D) None of these
Answer: (B)
Year: 2001 | Set: S1

Q72. Two point charges placed at a certain distance attract each other. When placed in water, force between them:
(A) Increases
(B) Decreases
(C) Remains same
(D) Becomes zero
Answer: (B)
Year: 2001 | Set: Z

Q73. When plates of a charged capacitor are separated further:
(A) Capacitance increases
(B) Capacitance decreases
(C) Voltage decreases
(D) Energy decreases
Answer: (B)
Year: 2001 | Set: Y

Q74. Potential due to a charged shell inside the shell is:
(A) Infinite
(B) Zero
(C) Constant
(D) Proportional to radius
Answer: (C)
Year: 2001 | Set: M

Q75. If the separation of plates of a parallel plate capacitor is doubled, its energy:
(A) Halved
(B) Doubled
(C) Unchanged
(D) Becomes four times
Answer: (B)
Year: 2001 | Set: Q

Q76. Which configuration gives zero potential at origin for two equal charges?
(A) On x-axis symmetrically
(B) On y-axis asymmetrically
(C) One positive, one negative at equal distances
(D) One at origin
Answer: (C)
Year: 2001 | Set: P

Q77. What is the energy density of an electric field E in vacuum?
(A) ε₀E²
(B) ½ε₀E²
(C) E²/2ε₀
(D) E²/ε₀
Answer: (B)
Year: 2001 | Set: X

Q78. For a parallel plate capacitor, what happens if dielectric is removed while connected to a battery?
(A) Capacitance increases
(B) Voltage remains constant
(C) Electric field decreases
(D) Charge remains constant
Answer: (B)
Year: 2001 | Set: Y

Q79. The potential difference between the plates of a capacitor is 10 V. If the distance is doubled keeping the charge constant, the new potential is:
(A) 5 V
(B) 20 V
(C) 10 V
(D) 2.5 V
Answer: (B)
Year: 2001 | Set: S2

Q80. If a dielectric of constant K is inserted between the plates of a capacitor, the potential:
(A) Increases
(B) Decreases
(C) Remains same
(D) Becomes zero
Answer: (B)
Year: 2001 | Set: Z

Q81. Capacitance is maximum when:
(A) Area is minimum, distance maximum
(B) Area maximum, distance minimum
(C) Area and distance both minimum
(D) Area and distance both maximum
Answer: (B)
Year: 2001 | Set: M

Q82. Which quantity does not change when a charged capacitor is disconnected from the battery?
(A) Charge
(B) Voltage
(C) Capacitance
(D) Energy
Answer: (A)
Year: 2001 | Set: Q

Q83. In a parallel plate capacitor, when distance is reduced to half, capacitance becomes:
(A) Double
(B) Half
(C) Four times
(D) Same
Answer: (A)
Year: 2001 | Set: P

Q84. Electric potential is related to electric field by:
(A) E = -dV/dr
(B) V = dE/dr
(C) E = dV/dr
(D) V = -dE/dr
Answer: (A)
Year: 2001 | Set: S

Q85. A capacitor is connected to battery and then disconnected. If distance between plates is increased:
(A) Capacitance decreases, voltage increases
(B) Voltage constant, energy increases
(C) Energy decreases
(D) Energy constant
Answer: (C)
Year: 2001 | Set: X

Q86. A capacitor stores 2 J energy at 100 V. Its capacitance is:
(A) 0.04 F
(B) 0.02 F
(C) 0.1 F
(D) 0.2 F
Answer: (B)
Year: 2001 | Set: Y

Q87. Insertion of dielectric affects:
(A) Charge
(B) Voltage
(C) Electric field
(D) All of these
Answer: (D)
Year: 2001 | Set: Z

Q88. Potential difference across capacitor is reduced to half. Energy becomes:
(A) One-fourth
(B) Half
(C) One-eighth
(D) Doubled
Answer: (A)
Year: 2001 | Set: P

Q89. For two equal charges placed symmetrically, the electric field at midpoint is:
(A) Zero
(B) Maximum
(C) Infinite
(D) Cannot be determined
Answer: (A)
Year: 2001 | Set: S

Q90. Electric potential at a point in space due to system of charges is:
(A) Scalar sum of potentials
(B) Vector sum of potentials
(C) Product of all charges
(D) Always zero
Answer: (A)
Year: 2001 | Set: Q

Q91. A dipole in uniform electric field experiences:
(A) Net force
(B) Net torque
(C) Displacement
(D) Both force and torque
Answer: (B)
Year: 2001 | Set: M

Q92. Dimensions of electric potential:
(A) ML²T⁻³A⁻¹
(B) ML²T⁻²A⁻¹
(C) MLT⁻²
(D) ML²T⁻³
Answer: (A)
Year: 2001 | Set: X

Q93. Capacitance between two infinite parallel plates is independent of:
(A) Distance
(B) Area
(C) Medium
(D) Thickness of plates
Answer: (D)
Year: 2001 | Set: Y

Q94. Electric field inside a charged spherical shell:
(A) Zero
(B) Maximum
(C) Infinite
(D) Uniform
Answer: (A)
Year: 2001 | Set: Q

Q95. Capacitance of parallel plate capacitor with dielectric inserted fully:
(A) C
(B) KC
(C) C/K
(D) K/C
Answer: (B)
Year: 2001 | Set: Z

Q96. The potential energy of two equal positive point charges separated by distance r is:
(A) Zero
(B) Negative
(C) Positive
(D) Infinite
Answer: (C)
Year: 2001 | Set: P

Q97. A charged conductor has constant potential throughout its surface because:
(A) Charges reside on surface
(B) Work done is zero in moving charge
(C) Electric field is zero inside
(D) All of these
Answer: (D)
Year: 2001 | Set: M

Q98. The electric field at the center of a uniformly charged ring is:
(A) Zero
(B) Maximum
(C) Minimum
(D) Infinite
Answer: (A)
Year: 2001 | Set: S2

Q99. Which of the following is true for equipotential surfaces?
(A) Electric field is tangent
(B) Electric field is normal
(C) Electric field is zero
(D) Electric field is variable
Answer: (B)
Year: 2001 | Set: Y

Q100. Which statement is correct for a charged conductor?
(A) Charge lies on surface
(B) Electric field inside is uniform
(C) Potential is not constant
(D) Energy is zero
Answer: (A)
Year: 2001 | Set: X

JEE MAINS QUESTIONS FROM THIS LESSON

Q1. Two point charges +3 μC and –3 μC are placed at a distance 2 m apart. The electric potential at the midpoint is:
(A) Zero
(B) Positive
(C) Negative
(D) Infinite
Answer: (A)
Year: 2025 | Shift: 1 | Set: A

Q2. A parallel plate capacitor with air between the plates has a capacitance of 8 μF. What will be the capacitance if the distance between the plates is reduced to half and the space between them is filled with a dielectric of constant 2?
(A) 8 μF
(B) 32 μF
(C) 16 μF
(D) 4 μF
Answer: (C)
Year: 2025 | Shift: 2 | Set: C

Q3. The energy stored in a 5 μF capacitor charged to a potential difference of 200 V is:
(A) 0.10 J
(B) 0.25 J
(C) 0.50 J
(D) 0.20 J
Answer: (C)
Year: 2024 | Shift: 1 | Set: B

Q4. A capacitor of capacitance C is connected across a battery of voltage V. The energy stored is given by:
(A) ½ CV
(B) CV
(C) ½ CV²
(D) V²/C
Answer: (C)
Year: 2024 | Shift: 2 | Set: A

Q5. Electric potential due to a point charge is:
(A) Directly proportional to distance
(B) Inversely proportional to square of distance
(C) Directly proportional to square of distance
(D) Inversely proportional to distance
Answer: (D)
Year: 2023 | Shift: 1 | Set: B

Q6. A dielectric slab of dielectric constant K is inserted into a charged capacitor after disconnecting the battery. The potential difference across the plates:
(A) Increases
(B) Decreases
(C) Remains unchanged
(D) Becomes zero
Answer: (B)
Year: 2023 | Shift: 2 | Set: C

Q7. If the plates of a parallel plate capacitor are moved farther apart, the capacitance:
(A) Increases
(B) Decreases
(C) Remains the same
(D) Becomes zero
Answer: (B)
Year: 2022 | Shift: 1 | Set: D

Q8. A conductor has charge Q and radius R. The potential at the surface is:
(A) kQ/R
(B) kQ/R²
(C) R/kQ
(D) Zero
Answer: (A)
Year: 2022 | Shift: 2 | Set: A

Q9. The energy stored in a capacitor per unit volume is called:
(A) Electric intensity
(B) Electric pressure
(C) Electric energy density
(D) Dielectric strength
Answer: (C)
Year: 2021 | Shift: 1 | Set: B

Q10. The electric potential at the center of a dipole is:
(A) Zero
(B) Maximum
(C) Minimum
(D) Infinite
Answer: (A)
Year: 2021 | Shift: 2 | Set: C

Q11. A parallel plate capacitor is charged and then disconnected from the battery. A dielectric slab is inserted. The energy of the capacitor:
(A) Increases
(B) Decreases
(C) Remains the same
(D) Becomes zero
Answer: (B)
Year: 2020 | Shift: 1 | Set: A

Q12. The unit of permittivity is:
(A) F/m
(B) C/V
(C) V/C
(D) N/C
Answer: (A)
Year: 2020 | Shift: 2 | Set: B

Q13. Capacitance of a spherical conductor is proportional to:
(A) 1/R²
(B) 1/R
(C) R
(D) R²
Answer: (C)
Year: 2019 | Shift: 1 | Set: A

Q14. Electric potential due to an electric dipole on its equatorial line varies as:
(A) 1/r
(B) 1/r²
(C) 1/r³
(D) r
Answer: (C)
Year: 2019 | Shift: 2 | Set: D

Q15. A capacitor is connected across a battery. The energy stored in it is:
(A) CV
(B) Q²/C
(C) ½ CV²
(D) QV
Answer: (C)
Year: 2018 | Shift: 1 | Set: A

Q16. In a system of charges, the potential energy of configuration depends on:
(A) Position of charges
(B) Mass of charges
(C) Acceleration
(D) Shape of container
Answer: (A)
Year: 2018 | Shift: 2 | Set: B

Q17. The capacitance of two capacitors connected in series is:
(A) C₁ + C₂
(B) C₁C₂/(C₁ + C₂)
(C) C₁ – C₂
(D) C₁C₂
Answer: (B)
Year: 2017 | Shift: 1 | Set: D

Q18. A point charge q is placed at the center of a conducting spherical shell. Electric potential inside the shell is:
(A) Zero
(B) Constant
(C) Varies with r
(D) Infinite
Answer: (B)
Year: 2017 | Shift: 2 | Set: C

Q19. The energy stored in a capacitor is:
(A) QV
(B) CV
(C) Q²/2C
(D) V²C
Answer: (C)
Year: 2016 | Shift: 1 | Set: A

Q20. A capacitor of 5 µF is connected to a 10 V battery. The energy stored is:
(A) 0.25 mJ
(B) 0.5 mJ
(C) 0.05 J
(D) 2.5 mJ
Answer: (D)
Year: 2016 | Shift: 2 | Set: B

Q21. A dielectric slab is inserted between the plates of a capacitor. The capacitance:
(A) Decreases
(B) Increases
(C) Remains same
(D) Becomes zero
Answer: (B)
Year: 2015 | Shift: 1 | Set: C

Q22. Capacitance of a system is independent of:
(A) Geometry
(B) Medium
(C) Potential difference
(D) Distance
Answer: (C)
Year: 2015 | Shift: 2 | Set: A

Q23. The potential energy of an electric dipole in uniform electric field is:
(A) pE sinθ
(B) pE cosθ
(C) –pE cosθ
(D) –pE sinθ
Answer: (C)
Year: 2014 | Shift: 1 | Set: D

Q24. Which of the following is correct regarding electric field lines and equipotential surfaces?
(A) They intersect at 45°
(B) They are parallel
(C) They are perpendicular
(D) They are random
Answer: (C)
Year: 2014 | Shift: 2 | Set: B

Q25. Electric field is the negative gradient of:
(A) Electric potential
(B) Electric flux
(C) Electric energy
(D) Electric charge
Answer: (A)
Year: 2013 | Shift: 1 | Set: C

Q26. The electric field just outside a charged conductor is:
(A) Parallel to the surface
(B) Perpendicular to the surface
(C) Zero
(D) Tangent to the surface
Answer: (B)
Year: 2013 | Shift: 2 | Set: A

Q27. Two equal charges are placed at a certain distance. The potential at the midpoint is:
(A) Zero
(B) Positive
(C) Negative
(D) Infinite
Answer: (B)
Year: 2012 | Shift: 1 | Set: B

Q28. A conductor is placed in a uniform electric field. The electric field inside the conductor is:
(A) Zero
(B) Same as outside
(C) Half of the outside field
(D) Infinity
Answer: (A)
Year: 2012 | Shift: 2 | Set: C

Q29. The dimensional formula of electric potential is:
(A) ML²T⁻³A⁻¹
(B) MLT⁻²
(C) ML²T⁻²
(D) MLT
Answer: (A)
Year: 2011 | Shift: 1 | Set: A

Q30. The potential due to an electric dipole at an axial point is proportional to:
(A) 1/r²
(B) 1/r³
(C) r
(D) 1/r
Answer: (B)
Year: 2011 | Shift: 2 | Set: B

Q31. Which one of the following increases the capacitance of a parallel plate capacitor?
(A) Increasing distance
(B) Decreasing plate area
(C) Using air as dielectric
(D) Inserting a dielectric slab
Answer: (D)
Year: 2010 | Shift: 1 | Set: C

Q32. The electric potential energy of a system of two like charges is:
(A) Negative
(B) Zero
(C) Positive
(D) Infinite
Answer: (C)
Year: 2010 | Shift: 2 | Set: A

Q33. For a parallel plate capacitor, if distance is doubled and area is halved, the capacitance becomes:
(A) One-fourth
(B) One-eighth
(C) Half
(D) Double
Answer: (B)
Year: 2009 | Shift: 1 | Set: B

Q34. A capacitor of capacitance C has energy U. If its capacitance becomes 2C at the same charge, new energy is:
(A) U/2
(B) U
(C) 2U
(D) 4U
Answer: (A)
Year: 2009 | Shift: 2 | Set: D

Q35. A point charge is placed at the center of a conducting spherical shell. Electric field inside the conductor is:
(A) kq/r²
(B) Zero
(C) Infinite
(D) Constant
Answer: (B)
Year: 2008 | Shift: 1 | Set: A

Q36. If the electric field is uniform, the potential varies:
(A) Linearly
(B) Quadratically
(C) Exponentially
(D) Logarithmically
Answer: (A)
Year: 2008 | Shift: 2 | Set: C

Q37. The energy stored in a capacitor per unit volume is given by:
(A) ε₀E²
(B) ½ε₀E²
(C) E²/ε₀
(D) 2ε₀E²
Answer: (B)
Year: 2007 | Shift: 1 | Set: D

Q38. A dielectric of dielectric constant K reduces the electric field by a factor of:
(A) 1/K
(B) K
(C) K²
(D) 1/K²
Answer: (A)
Year: 2007 | Shift: 2 | Set: B

Q39. Two capacitors C₁ and C₂ are in series. The total charge on the combination is:
(A) C₁V
(B) C₂V
(C) CV
(D) Same on both
Answer: (D)
Year: 2006 | Shift: 1 | Set: C

Q40. The electric field is always normal to:
(A) Current lines
(B) Equipotential surfaces
(C) Magnetic field lines
(D) None
Answer: (B)
Year: 2006 | Shift: 2 | Set: A

Q41. A capacitor is charged to a potential V and then disconnected. If the plates are pulled apart, the new energy is:
(A) Increases
(B) Decreases
(C) Remains same
(D) Zero
Answer: (A)
Year: 2005 | Shift: 1 | Set: B

Q42. A capacitor is said to be full when:
(A) It stores infinite charge
(B) It stores maximum energy
(C) The potential equals battery potential
(D) Charge becomes zero
Answer: (C)
Year: 2005 | Shift: 2 | Set: D

Q43. The value of electric potential at infinity is usually taken as:
(A) Zero
(B) One
(C) Infinity
(D) Negative
Answer: (A)
Year: 2004 | Shift: 1 | Set: A

Q44. What is the electric potential at a point due to electric dipole of moment p at distance r on axial line?
(A) Zero
(B) p/(4πε₀r²)
(C) p/(4πε₀r³)
(D) p/(4πε₀r)
Answer: (C)
Year: 2004 | Shift: 2 | Set: B

Q45. A conductor is placed in electrostatic equilibrium. The field inside is:
(A) Uniform
(B) Zero
(C) Infinite
(D) Non-zero constant
Answer: (B)
Year: 2003 | Shift: 1 | Set: C

Q46. Electric potential difference between two points is measured using:
(A) Voltmeter
(B) Ammeter
(C) Galvanometer
(D) Potentiometer
Answer: (A)
Year: 2003 | Shift: 2 | Set: D

Q47. A 3 μF capacitor is charged to 100 V. Energy stored is:
(A) 0.015 J
(B) 0.030 J
(C) 0.045 J
(D) 0.020 J
Answer: (B)
Year: 2002 | Shift: 1 | Set: B

Q48. The net electric field at the center of a uniformly charged spherical shell is:
(A) Maximum
(B) Zero
(C) Infinite
(D) Constant
Answer: (B)
Year: 2002 | Shift: 2 | Set: A

Q49. The unit of electric potential is:
(A) J/C
(B) N/C
(C) J
(D) C
Answer: (A)
Year: 2001 | Shift: 1 | Set: D

Q50. Capacitance does not depend upon:
(A) Area of plates
(B) Distance between plates
(C) Material between plates
(D) Amount of charge
Answer: (D)
Year: 2001 | Shift: 2 | Set: A

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

JEE ADVANCED QUESTIONS FROM THIS LESSON

JEE Advanced – Paper 1: Questions 1 to 17
Q1. A spherical conductor of radius R carries charge Q. The electric potential at a point inside the sphere (r < R) is:
(A) Zero
(B) kQ/R
(C) kQ/r
(D) kQ/r²
Answer: (B)
Year: 2025 | Paper: 1 | Set: 1

Q2. A point charge q is placed at a distance d from the center of a grounded conducting spherical shell of radius R (d > R). The induced charge on the inner surface is:
(A) Zero
(B) –q
(C) –qR/d
(D) –qR²/d²
Answer: (D)
Year: 2025 | Paper: 1 | Set: 2

Q3. Two capacitors of 2 μF and 4 μF are connected in series across 12 V. The energy stored in the system is:
(A) 16 μJ
(B) 24 μJ
(C) 32 μJ
(D) 8 μJ
Answer: (C)
Year: 2024 | Paper: 1 | Set: 1

Q4. An electric dipole is placed in a non-uniform electric field. It experiences:
(A) Only torque
(B) Only force
(C) Both torque and net force
(D) Neither force nor torque
Answer: (C)
Year: 2024 | Paper: 1 | Set: 2

Q5. The potential due to a dipole at a distance r from its center on the axial line is:
(A) ∝ 1/r
(B) ∝ 1/r²
(C) ∝ 1/r³
(D) ∝ r
Answer: (C)
Year: 2023 | Paper: 1 | Set: 1

Q6. A point charge is placed at the center of a conducting spherical shell. The electric field inside the shell is:
(A) Zero
(B) Infinite
(C) kq/r²
(D) Constant
Answer: (A)
Year: 2023 | Paper: 1 | Set: 2

Q7. A parallel plate capacitor is charged and then the battery is disconnected. If the plate separation increases, the potential difference:
(A) Increases
(B) Decreases
(C) Remains same
(D) Becomes zero
Answer: (A)
Year: 2022 | Paper: 1 | Set: 1

Q8. A capacitor of capacitance C is charged to potential V. If a dielectric slab of dielectric constant K is inserted, the energy stored becomes:
(A) ½CV²
(B) ½CV²/K
(C) ½KCV²
(D) KCV²
Answer: (B)
Year: 2022 | Paper: 1 | Set: 2

Q9. The electric potential at a point due to a dipole is zero. The electric field at that point:
(A) Is always zero
(B) Can’t be zero
(C) May or may not be zero
(D) Always infinite
Answer: (C)
Year: 2021 | Paper: 1 | Set: 1

Q10. Capacitance of a parallel plate capacitor is C. When a slab of dielectric constant K fills half the space, the new capacitance is:
(A) C
(B) 2C
(C) (K + 1)C/2
(D) KC
Answer: (C)
Year: 2021 | Paper: 1 | Set: 2

Q11. Electric field between two plates of parallel plate capacitor increases if:
(A) Distance is doubled
(B) Area is doubled
(C) Potential difference is increased
(D) Dielectric constant is increased
Answer: (C)
Year: 2020 | Paper: 1 | Set: 1

Q12. The potential at a point due to a system of charges is:
(A) Vector sum
(B) Scalar sum
(C) Cross product
(D) Zero always
Answer: (B)
Year: 2020 | Paper: 1 | Set: 2

Q13. The unit of electric potential energy is:
(A) J
(B) C
(C) V
(D) N/C
Answer: (A)
Year: 2019 | Paper: 1 | Set: 1

Q14. A charged conducting sphere is in electrostatic equilibrium. The potential inside:
(A) Increases with r
(B) Decreases with r
(C) Constant
(D) Zero
Answer: (C)
Year: 2019 | Paper: 1 | Set: 2

Q15. A dipole aligned at 30° to the direction of uniform electric field will experience:
(A) No torque
(B) Maximum torque
(C) Zero potential energy
(D) Some torque and negative potential energy
Answer: (D)
Year: 2018 | Paper: 1 | Set: 1

Q16. A 5 μF capacitor is charged to 10 V. Its stored energy is:
(A) 0.25 mJ
(B) 0.5 mJ
(C) 1 mJ
(D) 2 mJ
Answer: (B)
Year: 2018 | Paper: 1 | Set: 2

Q17. The dimensional formula for electric potential is:
(A) ML²T⁻³A⁻¹
(B) MLT⁻²
(C) ML²T⁻²
(D) MLT
Answer: (A)
Year: 2017 | Paper: 1 | Set: 1

JEE Advanced – Paper 2: Questions 18 to 34
Q18. Electric field is the negative gradient of:
(A) Charge
(B) Potential
(C) Distance
(D) Flux
Answer: (B)
Year: 2025 | Paper: 2 | Set: 1

Q19. A capacitor of capacitance C is connected to a battery and then disconnected. If a dielectric is inserted, energy becomes:
(A) Increases
(B) Decreases
(C) Remains same
(D) Zero
Answer: (B)
Year: 2025 | Paper: 2 | Set: 2

Q20. In a uniform electric field, the potential difference between two points depends on:
(A) Field strength and displacement
(B) Field strength only
(C) Distance only
(D) Field direction
Answer: (A)
Year: 2024 | Paper: 2 | Set: 1

Q21. A spherical shell is uniformly charged. The potential at its center is:
(A) kQ/R
(B) 2kQ/R
(C) Zero
(D) Infinite
Answer: (A)
Year: 2024 | Paper: 2 | Set: 2

Q22. A parallel plate capacitor with area A and plate separation d has capacitance C. If both A and d are doubled, the new capacitance is:
(A) C
(B) 2C
(C) C/2
(D) 4C
Answer: (A)
Year: 2023 | Paper: 2 | Set: 1

Q23. The energy stored in a capacitor is proportional to:
(A) V
(B) V²
(C) 1/V
(D) √V
Answer: (B)
Year: 2023 | Paper: 2 | Set: 2

Q24. A capacitor is connected across a battery. If the plate separation is increased, the electric field:
(A) Increases
(B) Decreases
(C) Remains same
(D) Becomes zero
Answer: (C)
Year: 2022 | Paper: 2 | Set: 1

Q25. An electric dipole is placed perpendicular to a uniform electric field. The torque on it is:
(A) Zero
(B) Maximum
(C) Infinite
(D) None
Answer: (B)
Year: 2022 | Paper: 2 | Set: 2

Q26. A system of charges has total potential energy U. If all distances are doubled, new energy is:
(A) 4U
(B) U/2
(C) U/4
(D) 2U
Answer: (C)
Year: 2021 | Paper: 2 | Set: 1

Q27. A spherical shell has charge Q. Electric field inside is:
(A) Zero
(B) Uniform
(C) Q/r²
(D) Infinite
Answer: (A)
Year: 2021 | Paper: 2 | Set: 2

Q28. Capacitance of two capacitors C and 2C connected in series is:
(A) C
(B) 3C
(C) 2C
(D) 2C/3
Answer: (D)
Year: 2020 | Paper: 2 | Set: 1

Q29. A dielectric constant increases the capacitance by a factor of:
(A) k
(B) 1/k
(C) k²
(D) √k
Answer: (A)
Year: 2020 | Paper: 2 | Set: 2

Q30. Electric potential at the center of an electric dipole is:
(A) Zero
(B) Maximum
(C) Minimum
(D) Equal to kq/r
Answer: (A)
Year: 2019 | Paper: 2 | Set: 1

Q31. A capacitor is connected across a 100 V source and stores 1 J energy. Capacitance is:
(A) 0.2 F
(B) 0.05 F
(C) 0.0002 F
(D) 0.00005 F
Answer: (C)
Year: 2019 | Paper: 2 | Set: 2

Q32. Electric potential energy is scalar because:
(A) Depends on mass
(B) Has no direction
(C) Follows superposition
(D) Cannot be negative
Answer: (B)
Year: 2018 | Paper: 2 | Set: 1

Q33. For constant charge, inserting dielectric in a capacitor causes energy to:
(A) Increase
(B) Decrease
(C) Stay same
(D) Go to zero
Answer: (B)
Year: 2018 | Paper: 2 | Set: 2

Q34. A dipole of moment p in electric field E at angle θ has torque:
(A) pE sinθ
(B) pE cosθ
(C) –pE sinθ
(D) –pE cosθ
Answer: (A)
Year: 2017 | Paper: 2 | Set: 1

PRACTICE SETS FROM THIS LESSON

Q1. The unit of electric potential is:
(A) J
(B) J/C
(C) C/V
(D) N/m
Answer: (B)

Q2. A dipole is placed in a uniform electric field. The net force on the dipole is:
(A) Maximum
(B) Minimum
(C) Zero
(D) Infinite
Answer: (C)

Q3. Which of the following factors increases the capacitance of a parallel plate capacitor?
(A) Decreasing plate area
(B) Increasing plate separation
(C) Using a dielectric
(D) Connecting to a battery
Answer: (C)

Q4. The capacitance of a capacitor is independent of:
(A) Area of plates
(B) Separation of plates
(C) Dielectric material
(D) Applied voltage
Answer: (D)

Q5. In the expression , what does U represent?
(A) Charge
(B) Current
(C) Energy stored in the capacitor
(D) Potential
Answer: (C)

Q6. A capacitor stores charge when:
(A) There is no potential difference
(B) Connected to a resistor
(C) Connected to a source of EMF
(D) Kept in open air
Answer: (C)

Q7. Which configuration has maximum equivalent capacitance?
(A) Capacitors in series
(B) Capacitors in parallel
(C) Capacitors at angle
(D) No combination
Answer: (B)

Q8. Electric field between two parallel plates is uniform because:
(A) Charges are concentrated at corners
(B) Plates are large and flat
(C) Electric potential is zero
(D) Plates are non-conducting
Answer: (B)

Q9. A charged spherical conductor has:
(A) Uniform charge throughout volume
(B) Charge only on surface
(C) Zero potential
(D) Charge in the center
Answer: (B)

Q10. A 2 µF capacitor is charged to 50 V. The energy stored is:
(A) 1.25 mJ
(B) 2.5 mJ
(C) 5.0 mJ
(D) 0.5 mJ
Answer: (A)

Q11. The potential due to an electric dipole at a point on its axial line is:
(A) Zero
(B) Positive
(C) Negative
(D) Depends on position
Answer: (D)

Q12. SI unit of capacitance is:
(A) Henry
(B) Farad
(C) Coulomb
(D) Volt
Answer: (B)

Q13. A capacitor blocks:
(A) DC only
(B) AC only
(C) Both AC and DC
(D) Neither AC nor DC
Answer: (A)

Q14. Electric field at the surface of a charged conductor is:
(A) Tangential
(B) Uniform
(C) Perpendicular to surface
(D) Zero
Answer: (C)

Q15. A dielectric inserted into a capacitor increases:
(A) Potential
(B) Capacitance
(C) Distance
(D) Voltage
Answer: (B)

Q16. Which pair affects capacitance of a parallel plate capacitor?
(A) Resistance and voltage
(B) Area and separation
(C) Area and current
(D) Distance and frequency
Answer: (B)

Q17. A capacitor stores energy in:
(A) Its magnetic field
(B) Its electric field
(C) Chemical form
(D) Mechanical stress
Answer: (B)

Q18. A charged capacitor is disconnected from the battery. On inserting dielectric:
(A) Voltage increases
(B) Voltage decreases
(C) Voltage remains same
(D) Charge changes
Answer: (B)

Q19. The electric potential due to a point charge q at a distance r is proportional to:
(A) 1/r²
(B) 1/r
(C) r
(D) r²
Answer: (B)

Q20. Potential energy of an electric dipole in a uniform field is minimum when:
(A) It is perpendicular to the field
(B) It is aligned opposite to field
(C) It is aligned with the field
(D) It lies in a circle
Answer: (C)

Q21. Which of the following is a scalar quantity?
(A) Electric field
(B) Electric potential
(C) Magnetic field
(D) Force
Answer: (B)

Q22. Energy density in a capacitor is proportional to:
(A) V
(B) V²
(C) E²
(D) 1/E
Answer: (C)

Q23. A dielectric reduces the electric field inside a capacitor because:
(A) It increases area
(B) It polarizes
(C) It blocks electrons
(D) It removes charge
Answer: (B)

Q24. The relation between electric field and electric potential is:
(A) E = V/d
(B) V = Ed
(C) E = dV/dr
(D) E = -dV/dr
Answer: (D)

Q25. Work done to move a charge in an equipotential surface is:
(A) Minimum
(B) Maximum
(C) Zero
(D) Constant
Answer: (C)

Q26. The value of electric field inside a conductor in electrostatic equilibrium is:
(A) Maximum
(B) Minimum
(C) Zero
(D) Equal to surface field
Answer: (C)

Q27. A conductor placed in external electric field has field lines:
(A) Inside
(B) Around
(C) Random
(D) Circular
Answer: (B)

Q28. Unit of electric flux:
(A) Nm²
(B) Nm²/C
(C) J/C
(D) C/V
Answer: (B)

Q29. Electric dipole consists of:
(A) Two negative charges
(B) Two equal and opposite charges
(C) Two positive charges
(D) Neutral particles
Answer: (B)

Q30. A capacitor acts as:
(A) Voltage regulator
(B) Energy dissipator
(C) Energy storer
(D) Conductor
Answer: (C)

Q31. What happens to potential energy if distance between opposite charges increases?
(A) Increases
(B) Decreases
(C) Becomes zero
(D) Doubles
Answer: (A)

Q32. Capacitance of a system depends on:
(A) Material and geometry
(B) Resistance
(C) Voltage
(D) Temperature
Answer: (A)

Q33. In a charged capacitor, electric field exists:
(A) Outside the plates
(B) Between the plates
(C) In battery
(D) In wire
Answer: (B)

Q34. Total work done in assembling a system of charges is equal to:
(A) Total current
(B) Total energy
(C) Potential energy of configuration
(D) Zero
Answer: (C)

Q35. A 10 μF capacitor is charged to 100 V and then disconnected from the battery. A dielectric of K = 5 is inserted. New potential difference across plates is:
(A) 100 V
(B) 500 V
(C) 20 V
(D) 200 V
Answer: (C)

Q36. A parallel plate capacitor has area 0.1 m² and separation 1 mm. Its capacitance in air is approximately:
(A) 8.85 μF
(B) 885 pF
(C) 0.885 μF
(D) 8.85 pF
Answer: (B)

Q37. The energy stored in a 6 μF capacitor charged to 200 V is:
(A) 0.12 J
(B) 0.24 J
(C) 0.36 J
(D) 1.2 J
Answer: (C)

Q38. Two capacitors 3 μF and 6 μF are connected in parallel across 12 V. Total energy stored is:
(A) 0.648 mJ
(B) 1.296 mJ
(C) 0.432 mJ
(D) 1.728 mJ
Answer: (D)

Q39. A 4 μF and a 12 μF capacitor are connected in series across 24 V. Charge on 4 μF capacitor is:
(A) 8 μC
(B) 12 μC
(C) 16 μC
(D) 18 μC
Answer: (C)

Q40. Electric potential at a point due to two equal charges at equal distances is:
(A) Zero
(B) 2kq/r
(C) kq/r
(D) kq/2r
Answer: (B)

Q41. A spherical conductor of radius 10 cm has charge 5 μC. Potential at its surface is (k = 9×10⁹):
(A) 4.5×10⁴ V
(B) 1.8×10⁴ V
(C) 9×10³ V
(D) 4.5×10³ V
Answer: (A)

Q42. Two point charges +3 μC and -3 μC are placed 1 m apart. The potential at the midpoint is:
(A) Zero
(B) Positive
(C) Negative
(D) Infinite
Answer: (A)

Q43. A dielectric slab of thickness t (< d) is inserted between plates of a capacitor separated by d. Effective capacitance becomes:
(A) ε₀A/d
(B) ε₀A/(d – t + t/K)
(C) ε₀AK/d
(D) ε₀Ad/K
Answer: (B)

Q44. Potential energy of a system of three equal charges at the corners of equilateral triangle is:
(A) Zero
(B) 3kq²/r
(C) √3kq²/r
(D) 3kq²/2r
Answer: (B)

Q45. A charged conductor is connected to an uncharged conductor. At equilibrium:
(A) Both have same charge
(B) Same potential
(C) Same capacitance
(D) Same field
Answer: (B)

Q46. Capacitance of a cylindrical capacitor increases if:
(A) Outer radius decreases
(B) Inner radius increases
(C) Length decreases
(D) Dielectric is inserted
Answer: (D)

Q47. In electrostatics, the electric field inside a hollow conductor is:
(A) Maximum
(B) Equal to surface field
(C) Zero
(D) Constant
Answer: (C)

Q48. Work done in moving 2 C charge across 5 V is:
(A) 2.5 J
(B) 10 J
(C) 0.4 J
(D) 7 J
Answer: (B)

Q49. If a parallel plate capacitor is connected to a battery and plate area is doubled, new charge is:
(A) Doubled
(B) Same
(C) Halved
(D) Zero
Answer: (A)

Q50. Two point charges +q and -q form a dipole. Electric field at equatorial point varies as:
(A) 1/r
(B) 1/r²
(C) 1/r³
(D) r²
Answer: (C)

Q51. Capacitance of a system with dielectric constant K becomes:
(A) C/K
(B) KC
(C) C + K
(D) C/K²
Answer: (B)

Q52. The electrostatic potential energy of a dipole in an external field is minimum when:
(A) Dipole is perpendicular to field
(B) Dipole is anti-parallel to field
(C) Dipole is aligned with field
(D) Dipole is in vacuum
Answer: (C)

Q53. A 100 μC charge moves through 10 V potential difference. Energy gained is:
(A) 1 mJ
(B) 10 mJ
(C) 0.1 mJ
(D) 100 mJ
Answer: (B)

Q54. Equipotential surfaces are always:
(A) Circular
(B) Spherical
(C) Perpendicular to electric field lines
(D) Along electric field lines
Answer: (C)

Q55. Capacitance is numerically equal to:
(A) Charge × potential
(B) Charge / potential
(C) Potential / charge
(D) Current × time
Answer: (B)

Q56. A capacitor of 2 μF is charged to 20 V. It is connected to another uncharged capacitor of 2 μF. Final potential is:
(A) 10 V
(B) 20 V
(C) 40 V
(D) 0 V
Answer: (A)

Q57. Which of the following has dimensions of electric potential?
(A) Work × charge
(B) Energy/charge
(C) Charge × voltage
(D) Voltage × time
Answer: (B)

Q58. Energy stored in a capacitor is halved if:
(A) Capacitance is doubled
(B) Voltage is doubled
(C) Voltage is halved
(D) Capacitance is halved
Answer: (C)

Q59. Charge stored on a capacitor is directly proportional to:
(A) Resistance
(B) Area
(C) Voltage
(D) Temperature
Answer: (C)

Q60. A capacitor is charged to potential V. On connecting to another identical uncharged capacitor, final energy is:
(A) Same
(B) Half
(C) Zero
(D) Double
Answer: (B)

Q61. If distance between capacitor plates is reduced by half, capacitance:
(A) Doubles
(B) Halves
(C) Becomes four times
(D) No change
Answer: (A)

Q62. A charged capacitor is disconnected. A dielectric inserted. Final energy becomes:
(A) Increases
(B) Decreases
(C) Same
(D) Infinite
Answer: (B)

Q63. Electric potential is negative of:
(A) Gradient of electric field
(B) Gradient of potential
(C) Work done per unit charge
(D) Line integral of electric field
Answer: (D)

Q64. Two point charges placed 1 m apart repel each other with 9 N. If medium’s K = 3, new force is:
(A) 27 N
(B) 3 N
(C) 9 N
(D) 1 N
Answer: (B)

Q65. The SI unit of permittivity ε₀ is:
(A) F/m
(B) C/V
(C) N/C
(D) C²/N·m²
Answer: (A)

Q66. A capacitor has capacitance 10 μF. It is charged to 20 V. Charge on it is:
(A) 0.2 C
(B) 2 × 10⁻⁴ C
(C) 2 × 10⁻³ C
(D) 5 C
Answer: (C)

Q67. Capacitance of an isolated spherical conductor is directly proportional to:
(A) Radius
(B) Radius²
(C) 1/radius
(D) Volume
Answer: (A)

Q68. A metallic spherical shell of radius R is given a charge Q. The electric field at a point inside the shell at distance r < R is:
(A) kQ/r²
(B) Zero
(C) kQ/R²
(D) kQ/r
Answer: (B)

Q69. A capacitor of capacitance C is connected across a battery of voltage V. If a dielectric of constant K is inserted keeping connection intact, the charge becomes:
(A) CV
(B) KCV
(C) CV/K
(D) Zero
Answer: (B)

Q70. A spherical shell has charge distributed uniformly on its surface. The potential at its center is:
(A) Zero
(B) kQ/R
(C) kQ/2R
(D) kQ/R²
Answer: (B)

Q71. A dipole of dipole moment p is placed in an electric field E at angle θ. The torque is given by:
(A) pE
(B) pE cosθ
(C) pE sinθ
(D) Zero
Answer: (C)

Q72. Work done in rotating a dipole from 0° to 180° in uniform electric field E is:
(A) 0
(B) pE
(C) –pE
(D) 2pE
Answer: (D)

Q73. A conducting sphere of radius R is charged to potential V. If radius is doubled, keeping charge same, new potential becomes:
(A) V
(B) V/2
(C) 2V
(D) V²
Answer: (B)

Q74. Capacitance of parallel plate capacitor becomes infinite if:
(A) Distance = 0
(B) Dielectric = 0
(C) Voltage = 0
(D) Area = 0
Answer: (A)

Q75. A spherical conductor has potential V at surface. What is the work done in bringing unit positive charge from infinity to center?
(A) Zero
(B) V
(C) 2V
(D) Depends on path
Answer: (B)

Q76. A capacitor of 10 μF is connected in series with 20 μF. Equivalent capacitance is:
(A) 30 μF
(B) 6.66 μF
(C) 10 μF
(D) 15 μF
Answer: (B)

Q77. A 20 μF capacitor is charged to 200 V and connected to uncharged 10 μF. Final potential difference:
(A) 100 V
(B) 133.33 V
(C) 200 V
(D) 66.67 V
Answer: (B)

Q78. A point P lies equidistant from two point charges +Q and -Q. The electric field at P is:
(A) Zero
(B) Along the dipole axis
(C) Perpendicular to dipole axis
(D) Infinite
Answer: (C)

Q79. A capacitor has plates of area A and distance d. Two dielectrics K₁ and K₂ fill half the space each. Capacitance becomes:
(A) ε₀A/d
(B) 2ε₀A/(d/K₁ + d/K₂)
(C) ε₀A(K₁ + K₂)/2d
(D) ε₀AK₁K₂/(K₁ + K₂)d
Answer: (B)

Q80. The energy stored in a spherical conductor of radius R and charge Q is:
(A) kQ²/2R
(B) kQ²/R
(C) kQ²/4R
(D) kQ²/3R
Answer: (A)

Q81. An isolated conductor of capacitance C is at potential V. If another uncharged conductor is brought nearby without touching, the potential:
(A) Increases
(B) Decreases
(C) Remains same
(D) Becomes zero
Answer: (B)

Q82. A system of charges is configured such that net electric field at a point is zero, but potential is non-zero. Which is true?
(A) Charges are equal and opposite
(B) Configuration is symmetric
(C) Field vectors cancel, potential adds
(D) Field and potential are always zero together
Answer: (C)

Q83. A capacitor stores 4 J energy at 100 V. Its capacitance is:
(A) 0.2 F
(B) 0.08 F
(C) 0.4 F
(D) 0.002 F
Answer: (B)

Q84. A charged capacitor is connected across a resistor R. The energy dissipated in resistor is equal to:
(A) 0
(B) Stored energy
(C) Half of stored energy
(D) Depends on R
Answer: (B)

Q85. A non-uniform electric field exists between capacitor plates. Which statement is correct?
(A) Capacitance is undefined
(B) Field depends on charge
(C) Field depends on position
(D) Field is still uniform
Answer: (C)

Q86. In electrostatics, a system with minimum potential energy is in:
(A) Equilibrium
(B) Stable equilibrium
(C) Unstable equilibrium
(D) Oscillation
Answer: (B)

Q87. A capacitor has constant charge. If distance between plates is increased, energy:
(A) Increases
(B) Decreases
(C) Remains same
(D) Becomes zero
Answer: (A)

Q88. A capacitor is charged to V and energy stored is U. If dielectric of K = 4 inserted, new energy is:
(A) U
(B) U/2
(C) U/4
(D) 4U
Answer: (C)

Q89. A point charge +q is at origin. What is the direction of equipotential surface?
(A) Radial
(B) Tangential
(C) Perpendicular to radial
(D) No direction
Answer: (C)

Q90. Energy density in a capacitor is calculated using:
(A) ε₀E²
(B) ½ε₀E²
(C) E²/2ε₀
(D) 2ε₀E
Answer: (B)

Q91. Capacitance of a conductor depends only on:
(A) Charge
(B) Potential
(C) Geometry
(D) Current
Answer: (C)

Q92. A dipole placed in external electric field E has energy –pE. Angle between p and E is:
(A) 0°
(B) 180°
(C) 90°
(D) 45°
Answer: (A)

Q93. A capacitor of 2 μF is connected to 1 kV source. Energy stored is:
(A) 1 J
(B) 0.5 J
(C) 0.2 J
(D) 2 J
Answer: (B)

Q94. A 5 μF capacitor charged to 100 V is connected to a 10 μF uncharged capacitor. Energy loss is:
(A) 0.08 J
(B) 0.06 J
(C) 0.04 J
(D) 0.02 J
Answer: (A)

Q95. A spherical conductor of radius R has charge Q. If radius becomes R/2, the potential:
(A) Doubles
(B) Halves
(C) Increases four times
(D) Decreases four times
Answer: (A)

Q96. A capacitor connected across a battery is removed and then connected to a resistor. Energy finally becomes:
(A) 0
(B) Stored in capacitor
(C) Stored in resistor
(D) Converted to heat
Answer: (D)

Q97. A thin metallic spherical shell has no charge. If a charge q is placed inside the shell, the induced charge on inner surface is:
(A) Zero
(B) +q
(C) –q
(D) Depends on radius
Answer: (C)

Q98. A dielectric with K = ∞ inserted in a capacitor leads to:
(A) Infinite capacitance
(B) Zero energy
(C) Zero field
(D) Infinite field
Answer: (A)

Q99. Capacitance of a spherical capacitor with inner radius a, outer b is:
(A) 4πε₀ab/(b – a)
(B) 4πε₀/(a – b)
(C) 4πε₀(b – a)/ab
(D) None
Answer: (A)

Q100. A spherical conductor is charged. The field just outside the surface is proportional to:
(A) 1/R²
(B) σ/ε₀
(C) R
(D) ε₀R²
Answer: (B)

Important Notice : The lessons and study materials up to July–August 2025 have been sent. Soon, after receiving feedback from teachers and students, we will deliver the latest and more innovative study materials for the upcoming months.

Important Notice : The lessons and study materials up to July–August 2025 have been sent. Soon, after receiving feedback from teachers and students, we will deliver the latest and more innovative study materials for the upcoming months.

Class 12 : Physics (English) – Chapter 2: Electrostatic Potential and Capacitance

EXPLANATION & SUMMARY

QUESTIONS FROM TEXTBOOK

OTHER IMPORTANT QUESTIONS FOR EXAMS

NEET QUESTIONS FROM THIS LESSON

JEE MAINS QUESTIONS FROM THIS LESSON

JEE ADVANCED QUESTIONS FROM THIS LESSON

PRACTICE SETS FROM THIS LESSON

MISCONCEPTIONS “ALERTS”

KNOWLEDGE WITH FUN

MNEMONICS

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