Class 12 : Physics (English) – Chapter 4: Moving Charges and Magnetism

EXPLANATION & SUMMARY

🔹 Introduction – Discovery of Magnetic Effect of Current

💡 Concept: Electricity and magnetism are deeply interlinked. In 1820, Hans Christian Oersted observed that a magnetic compass needle placed near a current-carrying conductor deflects. This proved that moving charges (current) produce magnetic fields.

✔️ This discovery led to development of modern electromagnetism and electrodynamics.

🔹 Force on a Moving Charge in Magnetic Field

When a particle of charge q moves with velocity v in a magnetic field B, it experiences a force:

⚡ F = q (v × B)

🔵 Direction: Perpendicular to both v and B, given by Right-Hand Rule.

🟢 Magnitude: F = qvBsinθ

🔴 If v ∥ B → F = 0

🟡 If v ⊥ B → F = qvB (maximum)

➡️ This force does no work on the charge (since always perpendicular to displacement).

🔹 Force on a Current-Carrying Conductor

A conductor carrying current I in magnetic field B experiences force:

⚡ F = BIL sinθ

Direction: Given by Fleming’s Left-Hand Rule.

Basis for working of motors.

🔹 Motion of a Charged Particle in Magnetic Field

If a charged particle (say electron) enters a uniform magnetic field:

✔️ Case 1: v ⊥ B → Circular motion

Radius: r = mv / qB

Time period: T = 2πm / qB (independent of v)

Frequency: ν = qB / (2πm) (cyclotron frequency)

✔️ Case 2: v at angle θ → Helical motion

💡 Applications:

Cyclotron (accelerator)

Mass spectrometer

🔹 Biot–Savart Law (Fundamental Law of Magnetostatics)

Gives magnetic field due to current element Idl at distance r:

⚡ dB = (μ₀ / 4π) × (Idl × r̂) / r²

μ₀ = 4π × 10⁻⁷ T·m/A (permeability).

✔️ Applications:

Magnetic field at center of circular loop:
B = μ₀I / (2R)

🔹 Ampere’s Circuital Law

⚡ ∮ B · dl = μ₀I_enclosed

This powerful law gives B for symmetrical current distributions:

Long straight conductor:
B = μ₀I / (2πr)

Solenoid (n turns per length):
B = μ₀nI inside, nearly uniform.

Toroid:
B = μ₀NI / (2πr)

🔹 Force Between Two Parallel Currents

Two infinitely long parallel wires carrying currents I₁ and I₂ separated by distance d:

⚡ F/L = μ₀I₁I₂ / (2πd)

✔️ Attract if currents are parallel
✔️ Repel if opposite

💡 Definition of 1 Ampere: The current which, if maintained in two infinitely long parallel conductors 1 m apart, produces force 2 × 10⁻⁷ N/m.

🔹 Torque on a Current Loop – Magnetic Dipole

A rectangular current loop in magnetic field behaves like a magnetic dipole.

Magnetic dipole moment: m = IA (I = current, A = area vector).

Torque: τ = m × B

Potential energy: U = –m·B

➡️ Basis of galvanometer working.

🔹 Moving Coil Galvanometer

✔️ Principle: Current loop in uniform B experiences torque → produces deflection.

Deflection ∝ current

Sensitivity increased by:

Increasing number of turns (N)

Increasing area (A)

Strong magnetic field (B)

✔️ Conversion:

Ammeter → by low resistance shunt

Voltmeter → by high resistance in series

🔹 Summary of Important Formulae

🔵 Force on charge: F = qvBsinθ
🟢 Force on conductor: F = BILsinθ
🔴 Radius: r = mv / qB
🟡 Frequency: ν = qB / (2πm)
✏️ Biot–Savart: dB = (μ₀/4π) (Idl sinθ) / r²
✔️ Ampere law: ∮B·dl = μ₀I
💡 Solenoid: B = μ₀nI
➡️ Toroid: B = μ₀NI / (2πr)
⚡ Force per length: F/L = μ₀I₁I₂ / (2πd)
🌿 Dipole moment: m = IA
🧠 Torque: τ = mBsinθ

✨ Summary (~300 words)

The chapter “Moving Charges and Magnetism” explores the intimate connection between current and magnetic field. Oersted’s experiment demonstrated that electric current produces a magnetic field.

A moving charge in a magnetic field experiences the Lorentz force F = q(v × B), maximum when perpendicular. Similarly, a current-carrying conductor experiences force F = BIL sinθ, forming basis of motors.

Charged particles move in circular or helical paths inside uniform magnetic fields, with cyclotron frequency ν = qB / (2πm), leading to accelerators and spectrometers.

The Biot–Savart law establishes relation between current and magnetic field. Ampere’s law simplifies field calculation for symmetrical cases like long wire, solenoid, and toroid.

Two current-carrying wires exert forces: parallel currents attract, opposite repel. This principle defines the unit ampere.

A current loop behaves like a magnetic dipole with moment m = IA, experiencing torque τ = m × B in uniform fields.

Finally, the moving coil galvanometer is an application, measuring small currents with high sensitivity. With modifications, it becomes an ammeter or voltmeter.

Thus, the chapter builds the foundation of electromagnetism, linking electricity and magnetism in a unified framework.

📝 Quick Recap

✔️ Oersted’s experiment → Current produces magnetic field.
✔️ Lorentz force: F = qvBsinθ.
✔️ Current-carrying conductor force: F = BILsinθ.
✔️ Charged particle in B → Circular/Helical motion.
✔️ Biot–Savart law → Magnetic field of current element.
✔️ Ampere’s law → Useful for solenoid, toroid, long wire.
✔️ Force between currents → Parallel attract, opposite repel.
✔️ Magnetic dipole → m = IA, torque τ = mBsinθ.
✔️ Galvanometer → Basis of ammeter, voltmeter.

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QUESTIONS FROM TEXTBOOK

Q4.1

A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 4.00 A. What is the magnitude of the magnetic field B at the centre of the coil?

Answer:
Formula:
B = (μ₀ N I) / (2R)

Where:
N = 100 turns
I = 4.0 A
R = 0.08 m
μ₀ = 4π × 10⁻⁷ T·m/A

Step 1: Substitute values
B = (4π × 10⁻⁷ × 100 × 4.0) / (2 × 0.08)

Step 2: Simplify numerator
= (1600π × 10⁻⁷) / 0.16

Step 3: Calculate
= (1600π × 10⁻⁷) / 0.16
= (10,000π × 10⁻⁷)
= 3.14 × 10⁻³ T

Final Answer:
B = 3.14 × 10⁻³ T

Q4.2

A long straight wire carries a current of 35 A. What is the magnitude of the field B at a point 20 cm from the wire?

Answer:
Formula:
B = (μ₀ I) / (2πr)

I = 35 A
r = 0.20 m
μ₀ = 4π × 10⁻⁷ T·m/A

Step 1: Substitute
B = (4π × 10⁻⁷ × 35) / (2π × 0.20)

Step 2: Simplify
= (140π × 10⁻⁷) / (0.40π)
= (140 × 10⁻⁷) / 0.40
= 3.5 × 10⁻⁵ T

Final Answer:
B = 3.5 × 10⁻⁵ T

Q4.3

A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of B at a point 2.5 m east of the wire.

Answer:
Formula:
B = (μ₀ I) / (2πr)

I = 50 A
r = 2.5 m

Step 1: Substitute
B = (4π × 10⁻⁷ × 50) / (2π × 2.5)

Step 2: Simplify
= (200π × 10⁻⁷) / (5π)
= 40 × 10⁻⁷
= 4 × 10⁻⁶ T

Direction:
Using Right-hand rule → Point is east of wire, current is north to south → field is vertically downward.

Final Answer:
B = 4 × 10⁻⁶ T downward

Q4.4

A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line?

Answer:
Formula:
B = (μ₀ I) / (2πr)

I = 90 A
r = 1.5 m

Step 1: Substitute
B = (4π × 10⁻⁷ × 90) / (2π × 1.5)

Step 2: Simplify
= (360π × 10⁻⁷) / (3π)
= 120 × 10⁻⁷
= 1.2 × 10⁻⁵ T

Direction:
Using right-hand rule → Current east to west, point is below → field direction is towards south.

Final Answer:
B = 1.2 × 10⁻⁵ T (south direction)

Q4.5

What is the magnitude of magnetic force per unit length on a wire carrying a current of 8.0 A and making an angle of 30° with the direction of a uniform magnetic field of 0.15 T?

Answer:
Formula:
F/L = B I sinθ

B = 0.15 T
I = 8.0 A
θ = 30°

Step 1: Substitute
F/L = 0.15 × 8 × sin30°

Step 2: Simplify
= 1.2 × 0.5
= 0.6 N/m

Final Answer:
F/L = 0.6 N/m

Q4.6

A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T. What is the force on the wire?

Answer:
Formula:
F = B I L sinθ

Here θ = 90° (perpendicular)

B = 0.27 T
I = 10 A
L = 0.03 m

Step 1: Substitute
F = 0.27 × 10 × 0.03 × 1

Step 2: Simplify
= 0.081 N

Final Answer:
F = 8.1 × 10⁻² N

Q4.7

Two long parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by 0.40 m. Estimate the force on a 10 cm length of wire A.

Answer:
Formula:
F/L = (μ₀ I₁ I₂) / (2πd)

I₁ = 8 A, I₂ = 5 A
d = 0.40 m
L = 0.10 m

Step 1: Substitute
F = (4π × 10⁻⁷ × 8 × 5 × 0.10) / (2π × 0.40)

Step 2: Simplify
= (160π × 10⁻⁷ × 0.10) / (0.80π)
= (16 × 10⁻⁷) / 0.80
= 2 × 10⁻⁶ N

Direction:
Attractive force (currents in same direction).

Final Answer:
F = 2 × 10⁻⁶ N (attractive)

Q4.8

A closely wound solenoid 80 cm long has 5 layers of winding of 400 turns each. The diameter of solenoid is 1.8 cm. If current = 3.0 A, estimate B inside solenoid.

Answer:
Formula:
B = μ₀ n I

Total turns = 5 × 400 = 2000
Length = 0.80 m
n = N/L = 2000 / 0.80 = 2500 turns/m

Step 1: Substitute
B = 4π × 10⁻⁷ × 2500 × 3

Step 2: Simplify
= (12π × 10⁻⁴)
≈ 3.77 × 10⁻³ T

Final Answer:
B = 3.77 × 10⁻³ T

Q4.9

A square coil side 10 cm, 20 turns, current = 12 A. Coil suspended vertically, normal makes 30° with horizontal magnetic field B = 0.80 T. Find torque.

Answer:
Formula:
τ = N I A B sinθ

Side = 0.10 m → A = (0.10)² = 0.01 m²
N = 20, I = 12 A, B = 0.80 T, θ = 30°

Step 1: Substitute
τ = 20 × 12 × 0.01 × 0.80 × sin30°

Step 2: Simplify
= 20 × 12 × 0.01 × 0.80 × 0.5
= 0.96 N·m

Final Answer:
τ = 0.96 N·m

Q4.10

Two moving coil meters M₁ and M₂ particulars:
M₁ → N = 30, A = 3.6 × 10⁻³ m², B = 0.25 T, k = same
M₂ → N = 42, A = 1.8 × 10⁻³ m², B = 0.50 T

Find ratio of:
(a) current sensitivity
(b) voltage sensitivity

Answer:
Formula (current sensitivity): Sᵢ = N A B / k

For M₁: = 30 × 3.6 × 10⁻³ × 0.25 = 0.027
For M₂: = 42 × 1.8 × 10⁻³ × 0.50 = 0.0378

Ratio Sᵢ₁ : Sᵢ₂ = 0.027 : 0.0378 = 0.714 : 1

(b) Voltage sensitivity = Current sensitivity × Resistance

Since resistance not given → assume equal → ratio same

Final Answer:
(a) 0.714 : 1
(b) 0.714 : 1

Q4.11

Uniform magnetic field 6.5 G = 6.5 × 10⁻⁴ T. Electron shot with v = 4.8 × 10⁶ m/s perpendicular to field. Find radius.

Formula:
r = (mv) / (eB)

m = 9.1 × 10⁻³¹ kg
v = 4.8 × 10⁶
e = 1.6 × 10⁻¹⁹ C
B = 6.5 × 10⁻⁴ T

Step 1: Substitute
r = (9.1 × 10⁻³¹ × 4.8 × 10⁶) / (1.6 × 10⁻¹⁹ × 6.5 × 10⁻⁴)

Step 2: Simplify numerator
= 4.368 × 10⁻²⁴

Denominator
= 1.04 × 10⁻²²

r = 0.042 m = 4.2 cm

Final Answer:
r = 4.2 cm

Q4.12

In Q4.11 find frequency of revolution of electron. Does answer depend on speed?

Formula:
f = eB / (2πm)

e = 1.6 × 10⁻¹⁹
B = 6.5 × 10⁻⁴
m = 9.1 × 10⁻³¹

Step 1: Substitute
f = (1.6 × 10⁻¹⁹ × 6.5 × 10⁻⁴) / (2π × 9.1 × 10⁻³¹)

Step 2: Simplify
= (1.04 × 10⁻²²) / (5.72 × 10⁻³¹)
≈ 1.82 × 10⁸ Hz

Dependence: No, independent of velocity.

Final Answer:
f = 1.82 × 10⁸ Hz, independent of speed

Q4.13

Circular coil 30 turns, radius 8.0 cm, current = 6.0 A, coil vertical in uniform field B = 1.0 T. Field lines at 60° to plane of coil. Find torque and work required.

Answer:
(a) Torque formula: τ = N I A B sinθ

N = 30
r = 0.08 m → A = πr² = π(0.08)² = 0.0201 m²
I = 6 A, B = 1.0 T, θ = 60°

Step 1: Substitute
τ = 30 × 6 × 0.0201 × 1 × sin60°

Step 2: Simplify
= 3.13 N·m

(b) Work done = 2 × τ = 6.26 J

Final Answer:
τ = 3.13 N·m
W = 6.26 J

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OTHER IMPORTANT QUESTIONS

(CBSE MODEL QUESTION PAPER)

ESPECIALLY MADE FROM THIS LESSON ONLY

Section A (Q1 – Q18, 1 Mark Each)

Q1. Write the expression for the force on a moving charge in a magnetic field.
Answer:
F = q (v × B) = qvB sinθ

Q2. A proton and an electron enter a uniform magnetic field with same speed perpendicular to the field. Compare their radii of circular paths.
Answer:
r = mv / (qB) → Since mₚ >> mₑ, radius of proton >> radius of electron.

Q3. State Ampere’s Circuital Law.
Answer:
The line integral of the magnetic field B around a closed path is equal to μ₀ times the total current enclosed.
∮ B · dl = μ₀ Iₑₙc

Q4. Define current sensitivity of a moving coil galvanometer.
Answer:
Deflection per unit current in galvanometer = Current sensitivity = θ/I = (NAB)/k

Q5. Name the physical quantity whose SI unit is Tesla.
Answer:
Magnetic field (B).

Q6. Write expression for magnetic field at the centre of a circular coil carrying current.
Answer:
B = (μ₀ N I) / (2R)

Q7. Why do two parallel wires carrying current in same direction attract each other?
Answer:
Each wire produces a magnetic field that exerts a force on the other. Force is attractive if currents are parallel.

Q8. A long straight conductor carries current I. Write expression for magnetic field at a distance r from it.
Answer:
B = μ₀ I / (2πr)

Q9. Write one factor on which torque on a current carrying coil in uniform B depends.
Answer:
Depends on number of turns (N), current (I), area (A), magnetic field (B), and sinθ.

Q10. A straight wire along north–south direction carries current from south to north. Find direction of B at a point above the wire.
Answer:
Using right-hand rule → Direction is towards east.

Q11. What is the unit of current sensitivity of galvanometer?
Answer:
rad/A

Q12. What is the unit of voltage sensitivity of galvanometer?
Answer:
rad/V

Q13. Define Biot–Savart Law.
Answer:
It gives magnetic field due to a small current element:
dB = (μ₀/4π) × (I dl × r̂) / r²

Q14. Write expression for force between two parallel conductors.
Answer:
F/L = μ₀ I₁ I₂ / (2πd)

Q15. What is the nature of force between two parallel conductors carrying current in opposite directions?
Answer:
Repulsive.

Q16. What is the direction of magnetic moment of a current carrying coil?
Answer:
Perpendicular to plane of coil, given by right-hand rule.

Q17. A beam of alpha particles enters perpendicular to B. What is the shape of path?
Answer:
Circular path.

Q18. Write SI unit of magnetic permeability μ₀.
Answer:
N A⁻²

Section B (Q19 – Q23, 2 Marks Each)

Q19. A proton of charge 1.6 × 10⁻¹⁹ C enters B = 0.5 T with v = 2 × 10⁵ m/s perpendicular to field. Calculate radius of its path.
Answer:
r = mv / (qB)
= (1.67 × 10⁻²⁷ × 2 × 10⁵) / (1.6 × 10⁻¹⁹ × 0.5)
= 2.09 × 10⁻² m = 2.1 cm

Q20. Derive expression for torque on a rectangular coil in uniform B.
Answer:
Torque τ = Force × perpendicular distance
= N I A B sinθ

Q21. Two wires 5 m long separated by 10 cm carry 10 A each in same direction. Find force between them.
Answer:
F/L = μ₀ I₁ I₂ / (2πd)
= (4π × 10⁻⁷ × 10 × 10) / (2π × 0.10)
= 2 × 10⁻⁴ N/m
F = 5 × 2 × 10⁻⁴ = 1 × 10⁻³ N, attractive

Q22. A galvanometer has resistance 20 Ω, shows full deflection at 2 mA. How will you convert it into an ammeter of range 5 A?
Answer:
Shunt resistance Rs = Ig G / (I – Ig)
= (2 × 10⁻³ × 20) / (5 – 0.002)
≈ 0.008 / 4.998 ≈ 0.0016 Ω

Q23. State working principle of cyclotron.
Answer:
A charged particle can be accelerated in a circular path by using perpendicular electric and magnetic fields at resonance frequency.

Section C (Q24 – Q28, 3 Marks Each)

Q24. Derive expression for magnetic field due to a straight conductor of finite length using Biot–Savart law.
Answer:
B = (μ₀ I / 4πr)(sinθ₁ + sinθ₂)

Q25. A square coil of side 20 cm, 100 turns, current = 2 A placed in B = 0.2 T with its plane parallel to field. Find torque.
Answer:
τ = N I A B sinθ
= 100 × 2 × (0.2 × 0.2) × 0.2 × sin90°
= 100 × 2 × 0.04 × 0.2
= 1.6 N·m

Q26. Explain construction and working of a moving coil galvanometer.
Answer:

Rectangular coil suspended in uniform B.

Current produces torque τ = NIBA sinθ.

Restoring torque = kθ.

At equilibrium, θ ∝ I.

Scale calibrated to measure current.

Q27. A solenoid length 0.5 m has 2000 turns, current 5 A. Find B inside solenoid.
Answer:
n = N/L = 2000/0.5 = 4000 turns/m
B = μ₀ n I
= 4π × 10⁻⁷ × 4000 × 5
= 2.51 × 10⁻² T

Q28. A circular coil of radius 0.1 m, 50 turns carries 3 A current. Find magnetic moment and field at centre.
Answer:
Magnetic moment M = NIA
= 50 × 3 × π(0.1)²
= 50 × 3 × 0.0314 = 4.71 A·m²

Field B = μ₀ N I / (2R)
= (4π × 10⁻⁷ × 50 × 3) / (0.2)
= 9.42 × 10⁻⁴ T

Section D (Q29 – Q31, 4 Marks Each)

Q29. Derive expression for magnetic field at the centre of a circular coil using Biot–Savart law.
Answer:
B = μ₀ N I / (2R)
(Derivation: integrate current element around circle, symmetry → only perpendicular components add.)

Q30. An electron of energy 1 keV moves perpendicular to B = 0.04 T. Find frequency of revolution.
Answer:
K.E. = ½ mv² = 1 keV = 1000 × 1.6 × 10⁻¹⁹ = 1.6 × 10⁻¹⁶ J
v = √(2K/m) = √(2 × 1.6 × 10⁻¹⁶ / 9.1 × 10⁻³¹)
= 1.88 × 10⁷ m/s

Frequency f = eB / (2πm)
= (1.6 × 10⁻¹⁹ × 0.04) / (2π × 9.1 × 10⁻³¹)
= 1.12 × 10⁹ Hz

Q31. Explain the principle and working of a cyclotron with neat diagram.
Answer:

Principle: A charged particle can be accelerated in a spiral path using a perpendicular B and alternating electric field at cyclotron frequency.

Construction: Two Ds, magnetic field perpendicular, high frequency AC source applied.

Working: Particle accelerated each time it crosses gap, path radius increases, energy increases.

Section E (Q32 – Q35, 5 Marks Each)

Q32. Derive expression for force between two infinitely long parallel conductors and hence define 1 Ampere.
Answer:
F/L = μ₀ I₁ I₂ / (2πd)
1 Ampere = current when two conductors 1 m apart exert force 2 × 10⁻⁷ N/m on each other.

Q33. (Case-Based)
A solenoid of length 1 m and 1000 turns carries 2 A current. A wire of length 0.05 m inside solenoid is perpendicular to axis.
(a) Find magnetic field inside solenoid.
(b) Find force on wire if current = 1 A.
(c) State nature of force.

Answer:
(a) B = μ₀ n I = 4π × 10⁻⁷ × 1000 × 2 / 1 = 2.51 × 10⁻³ T
(b) F = BIL = 2.51 × 10⁻³ × 1 × 0.05 = 1.25 × 10⁻⁴ N
(c) Perpendicular force.

Q34. Explain conversion of galvanometer into voltmeter with necessary circuit and derivation.
Answer:

Connect high resistance (multiplier) in series.

V = Ig(G + R)

Range increased by choosing R.

Q35. A circular coil of 50 turns, radius 0.2 m, current 5 A is placed in a uniform magnetic field of 0.3 T at 30° with its plane.
(a) Find torque on coil.
(b) Find work required to turn coil from 0° to 90°.

Answer:
Area A = πr² = 0.1256 m²
M = NIA = 50 × 5 × 0.1256 = 31.4 A·m²

(a) τ = MB sinθ = 31.4 × 0.3 × sin30° = 4.71 N·m
(b) Work = MB(cosθ₁ – cosθ₂) = 31.4 × 0.3 (cos0 – cos90) = 9.42 J

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NEET QUESTIONS FROM THIS LESSON

Question 1: A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its plates is increasing at a constant rate with time. The magnetic field arising due to displacement current is:
🔵 (A) Non-zero everywhere, maximum at the rim
🟢 (B) Zero between plates, non-zero outside
🟠 (C) Zero at all places
🔴 (D) Constant between plates, zero outside
Answer: (A) Non-zero everywhere, maximum at the rim
Year: 2025 | Set/Shift: NEET UG, Morning Shift (NTA)

Question 2: An electron (mass 9×10^−31 kg, charge 1.6×10^−19 C) moves with speed c/100 into a uniform B = 9×10^−4 T perpendicular to its velocity. An electric field is applied so that the electron goes undeflected. Then:
🔵 (A) E ∥ B, 27×10² V/m
🟢 (B) E ∥ B, 27×10⁴ V/m
🟠 (C) E ⟂ B, 27×10⁴ V/m
🔴 (D) E ⟂ B, 27×10² V/m
Answer: (D) E ⟂ B, 27×10² V/m
Year: 2025 | Set/Shift: NEET UG, Evening Shift (NTA)

Question 3: Two small circular copper coils carry 2 A each; their radii are in the ratio 1:2. The ratio of their magnetic moments (small : large) is:
🔵 (A) 2:1
🟢 (B) 4:1
🟠 (C) 1:4
🔴 (D) 1:2
Answer: (C) 1:4
Year: 2025 | Set/Shift: NEET UG, Evening Shift (NTA)

Question 4: A tightly wound 100-turn coil of radius 10 cm carries 7 A. The magnetic field at the centre is:
🔵 (A) 44 mT
🟢 (B) 4.4 T
🟠 (C) 4.4 mT
🔴 (D) 44 T
Answer: (C) 4.4 mT
Year: 2024 | Set/Shift: NEET UG, Set Q1 (Morning)

Question 5: A parallel-plate capacitor is charged through a resistor by a battery. If I is the conduction current in the circuit, then in the gap between the plates:
🔵 (A) No current exists
🟢 (B) Displacement current of magnitude I flows in the same direction
🟠 (C) Displacement current of magnitude I flows in opposite direction
🔴 (D) Displacement current > I, random direction
Answer: (B) Displacement current of magnitude I flows in the same direction
Year: 2024 | Set/Shift: NEET UG, Set Q2 (Evening)

Question 6: A 2 m long wire (mass 250 g) is horizontal in a uniform horizontal field B = 0.7 T. The current needed to support it magnetically (g = 9.8 m/s²) is:
🔵 (A) 2.45 A
🟢 (B) 2.25 A
🟠 (C) 2.75 A
🔴 (D) 1.75 A
Answer: (D) 1.75 A
Year: 2023 | Set/Shift: NEET UG (Manipur), Morning

Question 7: Uniform E and B are along the same direction. An electron is projected along the fields. It will have:
🔵 (A) Right-turn motion
🟢 (B) Left-turn motion
🟠 (C) Decreasing speed
🔴 (D) Increasing speed
Answer: (D) Increasing speed
Year: 2023 | Set/Shift: NEET UG (Manipur), Evening

Question 8: A straight wire of length L along +x carries current I in magnetic field B = (2î + 3ĵ − 4k̂) T. Magnitude of magnetic force on the wire is:
🔵 (A) 2IL
🟢 (B) 3IL
🟠 (C) 4IL
🔴 (D) 5IL
Answer: (D) 5IL
Year: 2023 | Set/Shift: NEET UG, Set N2

Question 9: A closely packed coil has 1000 turns; average radius 62.8 cm. If current is 1 A, magnetic field at centre is nearly:
🔵 (A) 0.10 mT
🟢 (B) 1.0 mT
🟠 (C) 10 mT
🔴 (D) 0.10 T
Answer: (B) 1.0 mT
Year: 2022 | Set/Shift: NEET UG, Phase 2 (Set S1)

Question 10: Magnetic field lines due to an infinitely long straight current-carrying conductor are:
🔵 (A) Straight, parallel to the wire
🟢 (B) Radial straight lines
🟠 (C) Concentric circles about the wire
🔴 (D) Spirals along the wire
Answer: (C) Concentric circles about the wire
Year: 2022 | Set/Shift: NEET UG, Phase 2 (Set T2)

Question 11: Two very long, parallel conductors A and B, 10 cm apart, carry 5 A and 10 A in the same direction. Force per unit length between them is:
🔵 (A) 1×10⁻⁵ N/m
🟢 (B) 1×10⁻⁴ N/m
🟠 (C) 5×10⁻⁴ N/m
🔴 (D) 2×10⁻³ N/m
Answer: (B) 1×10⁻⁴ N/m
Year: 2022 | Set/Shift: NEET UG, Phase 2 (Set T1)

Question 12: On the axis of a loop (R = 1 m, I = √2 A) at x = 1 m, the magnetic field is:
🔵 (A) 3.14×10⁻⁷ T
🟢 (B) 3.14×10⁻⁶ T
🟠 (C) 6.28×10⁻⁷ T
🔴 (D) 6.28×10⁻⁶ T
Answer: (A) 3.14×10⁻⁷ T
Year: 2022 | Set/Shift: NEET UG, Phase 2 (Set P2)

Question 13: A long solenoid has 100 turns per mm and carries 1 A. The magnetic field at its centre is about:
🔵 (A) 0.0126 T
🟢 (B) 0.126 T
🟠 (C) 1.26 T
🔴 (D) 12.6 T
Answer: (B) 0.126 T
Year: 2022 | Set/Shift: NEET UG, Phase 1 (Morning)

Question 14: Statement I: Biot–Savart law gives magnetic field of an infinitesimal current element (Idl) only.
Statement II: It is analogous to Coulomb’s inverse-square law with Idl as scalar source and q as vector source.
🔵 (A) I true, II true, II explains I
🟢 (B) I true, II true, II doesn’t explain I
🟠 (C) I true, II false
🔴 (D) I false, II true
Answer: (C) I true, II false
Year: 2022 | Set/Shift: NEET UG, Phase 1 (Evening)

Question 15: For a long straight wire of circular cross-section with uniformly distributed current, the magnetic field B(r) varies as:
🔵 (A) B ∝ r (inside); B ∝ 1/r (outside)
🟢 (B) B ∝ 1/r (inside); B ∝ r (outside)
🟠 (C) B constant (inside); zero (outside)
🔴 (D) B ∝ r^2 (everywhere)
Answer: (A) B ∝ r (inside); B ∝ 1/r (outside)
Year: 2022 | Set/Shift: NEET UG, Phase 1 (Set S2)

Question 16: An electron at distance 0.20 m from a long straight wire (I = 5 A) moves parallel to it with 10⁵m/s. The force on the electron is nearest to:
🔵 (A) 8×10⁻²⁰ N
🟢 (B) 8×10⁻¹⁹ N
🟠 (C) 8×10⁻¹⁸ N
🔴 (D) 8×10−¹⁷ N
Answer: (A) 8×10⁻²⁰ N
Year: 2021 | Set/Shift: NEET UG, Evening (Set M2)

Question 17: A long solenoid of length 0.50 m with 100 turns carries 2.5 A. The magnetic field at its centre is:
🔵 (A) 3.14×10⁻⁴ T
🟢 (B) 6.28×10⁻⁴ T
🟠 (C) 1.26×10⁻³ T
🔴 (D) 2.00×10⁻³ T
Answer: (B) 6.28×10⁻⁴ T
Year: 2020 | Set/Shift: NEET UG, Morning (Set N1)

Question 18: Ionized H atoms and α-particles enter a uniform magnetic field with the same momentum. The ratio of their orbit radii r_H : r_α is:
🔵 (A) 1:2
🟢 (B) 2:1
🟠 (C) 1:1
🔴 (D) 1:4
Answer: (B) 2:1
Year: 2019 | Set/Shift: NEET UG, Set P2

Question 19: A long wire bent into one circular turn gives field B at the centre. If bent into n turns (same length), the field at the centre becomes:
🔵 (A) B/n
🟢 (B) B
🟠 (C) nB
🔴 (D) n^2B
Answer: (C) nB
Year: 2016 | Set/Shift: NEET UG, Phase 2 (Set X)

Question 20: A long straight wire of radius a carries uniform current I. The ratio B(a/2) : B(2a) equals:
🔵 (A) 1:1
🟢 (B) 1:2
🟠 (C) 2:1
🔴 (D) 3:1
Answer: (A) 1:1
Year: 2016 | Set/Shift: NEET UG, Phase 1 (Set M)

Question 21: A metallic rod of mass per unit length 0.5 kg/m rests on a smooth plane inclined at 30°. A vertical magnetic field of 0.25 T acts. The current in the rod needed to keep it stationary is:
🔵 (A) 5 A
🟢 (B) 10 A
🟠 (C) 20 A
🔴 (D) 40 A
Answer: (B) 10 A
Year: 2018 | Set/Shift: NEET UG, Set Q1

Question 22: A moving-coil galvanometer has current sensitivity 5 div/mA and voltage sensitivity 20 div/V. The galvanometer resistance is:
🔵 (A) 1 kΩ
🟢 (B) 250 Ω
🟠 (C) 4 kΩ
🔴 (D) 100 Ω
Answer: (B) 250 Ω
Year: 2018 | Set/Shift: NEET UG, Set R2

Question 23: Three long parallel wires carry equal currents I in the same direction; the middle wire is equidistant from the outer two. The magnitude of force per unit length on the middle wire is:
🔵 (A) μ₀I²/πd (towards either side)
🟢 (B) Zero
🟠 (C) μ₀I²/2πd (towards either side)
🔴 (D) μ₀I²/4πd (towards either side)
Answer: (B) Zero
Year: 2017 | Set/Shift: NEET UG, Set S1

Question 24: A cylindrical conductor of radius R carries uniform current. The correct plot of |B| vs distance r from axis is:
🔵 (A) Linear rise inside, 1/r outside
🟢 (B) 1/r inside, linear rise outside
🟠 (C) Constant inside, zero outside
🔴 (D) Linear everywhere
Answer: (A) Linear rise inside, 1/r outside
Year: 2019 | Set/Shift: NEET UG, Set N2

Question 25: A square loop carrying current i is coplanar and near a long straight current I. The net force on the loop is:
🔵 (A) Zero
🟢 (B) Attractive towards wire
🟠 (C) Repulsive from wire
🔴 (D) Depends on i/I ratio only
Answer: (B) Attractive towards wire
Year: 2020 | Set/Shift: NEET UG, Set O1

Question 26: A straight wire of length 0.5 m carrying 1.2 A is placed in a magnetic field of 2 T making an angle 60°. The force experienced is:
🔵 (A) 1.2 N
🟢 (B) 0.6 N
🟠 (C) 1.0 N
🔴 (D) 0.8 N
Answer: (A) 1.2 N
Year: 2015 | Set/Shift: AIPMT, Set P (Official)

Question 27: An electron of charge −e enters a magnetic field B with velocity v perpendicular to B. Its path is:
🔵 (A) Helical with constant pitch
🟢 (B) Circular
🟠 (C) Parabolic
🔴 (D) Straight line
Answer: (B) Circular
Year: 2014 | Set/Shift: AIPMT, Code T (Official)

Question 28: The unit of magnetic permeability μ0 is:
🔵 (A) N A⁻²
🟢 (B) Tesla m² A⁻¹
🟠 (C) H m⁻¹
🔴 (D) All of these
Answer: (D) All of these
Year: 2013 | Set/Shift: AIPMT, Set Q (Official)

Question 29: In a long straight solenoid carrying current, the magnetic field lines:
🔵 (A) Are circular outside
🟢 (B) Are parallel and uniform inside
🟠 (C) Form closed loops through solenoid
🔴 (D) All of these
Answer: (D) All of these
Year: 2012 | Set/Shift: AIPMT, Single Sitting (Official)

Question 30: A proton moving perpendicular to a uniform magnetic field of 1 T describes a circle of radius 1 cm. Its speed is: (Charge = 1.6×10^−19 C, mass = 1.67×10^−27 kg)
🔵 (A) 9.6×10⁵ m/s
🟢 (B) 9.6×10⁶ m/s
🟠 (C) 9.6×10⁷ m/s
🔴 (D) 9.6×10⁸ m/s
Answer: (B) 9.6×10⁶ m/s
Year: 2011 | Set/Shift: AIPMT, Single Sitting (Official)

Question 31: The SI unit of magnetic field intensity H is:
🔵 (A) A m⁻¹
🟢 (B) N A⁻¹
🟠 (C) T m
🔴 (D) Wb m⁻²
Answer: (A) A m⁻¹
Year: 2010 | Set/Shift: AIPMT, Code A (Official)

Question 32: The magnetic dipole moment of a current-carrying loop does not depend upon:
🔵 (A) Shape of loop
🟢 (B) Current
🟠 (C) Area
🔴 (D) Number of turns
Answer: (A) Shape of loop
Year: 2009 | Set/Shift: AIPMT, Code B (Official)

Question 33: A current flows in a circular loop. Magnetic field at the centre is B. If the loop is made double-turn with same current, field becomes:
🔵 (A) 2B
🟢 (B) 4B
🟠 (C) B/2
🔴 (D) B
Answer: (A) 2B
Year: 2008 | Set/Shift: AIPMT, Single Sitting (Official)

Question 34: Ampere’s circuital law is given by:
🔵 (A) ∮ B·dl = μ0I
🟢 (B) ∮ E·dl = 0
🟠 (C) ∮ B·dl = μ0ε0 dΦE/dt
🔴 (D) ∮ E·dl = −dΦB/dt
Answer: (A) ∮ B·dl = μ0I
Year: 2007 | Set/Shift: AIPMT, Official

Question 35: The value of μ0/4π is:
🔵 (A) 10^−9 Tm/A
🟢 (B) 10^−7 Tm/A
🟠 (C) 10^−6 Tm/A
🔴 (D) 10^−8 Tm/A
Answer: (B) 10^−7 Tm/A
Year: 2006 | Set/Shift: AIPMT, Official

Question 36: Magnetic field inside a long solenoid is:
🔵 (A) μ0nI
🟢 (B) μ0I/2πr
🟠 (C) μ0NIA/2R
🔴 (D) Zero
Answer: (A) μ0nI
Year: 2005 | Set/Shift: AIPMT, Official

Question 37: A bar magnet is equivalent to:
🔵 (A) A pair of magnetic charges
🟢 (B) A solenoid carrying current
🟠 (C) Both of these
🔴 (D) None of these
Answer: (C) Both of these
Year: 2004 | Set/Shift: AIPMT, Single Sitting (Official)

Question 38: The magnetic field at a distance r from a long straight current-carrying wire is:
🔵 (A) μ0I/2πr
🟢 (B) μ0nI
🟠 (C) μ0NI/2R
🔴 (D) Zero
Answer: (A) μ0I/2πr
Year: 2003 | Set/Shift: AIPMT, Code T (Official)

Question 39: The direction of magnetic field produced by a straight current-carrying wire is given by:
🔵 (A) Fleming’s left-hand rule
🟢 (B) Fleming’s right-hand rule
🟠 (C) Right-hand thumb rule
🔴 (D) Lenz’s law
Answer: (C) Right-hand thumb rule
Year: 2002 | Set/Shift: AIPMT, Single Sitting (Official)

Question 40: The magnetic field at the centre of a circular coil of radius R and N turns carrying current I is:
🔵 (A) μ0NI/2R
🟢 (B) μ0I/2πR
🟠 (C) μ0NIA/2R²
🔴 (D) Zero
Answer: (A) μ0NI/2R
Year: 2001 | Set/Shift: AIPMT, Code A (Official)

Question 41: The force per unit length between two parallel wires carrying equal currents I in the same direction and separated by distance d is:
🔵 (A) μ₀I²/2πd
🟢 (B) μ₀I²/4πd
🟠 (C) Zero
🔴 (D) 2μ₀I²/πd
Answer: (A) μ₀I²/2πd
Year: 2000 | Set/Shift: AIPMT, Single Sitting (Official)

Question 42: The SI unit of magnetic flux is:
🔵 (A) Weber
🟢 (B) Tesla
🟠 (C) Henry
🔴 (D) Joule
Answer: (A) Weber
Year: 1999 | Set/Shift: AIPMT, Official

Question 43: The force on a current element Idl in magnetic field B is:
🔵 (A) Idl·B
🟢 (B) IdlB sinθ
🟠 (C) Idl × B
🔴 (D) Zero
Answer: (C) Idl × B
Year: 1998 | Set/Shift: PMT, Official

Question 44: The unit of magnetic induction is:
🔵 (A) Weber/m²
🟢 (B) Tesla
🟠 (C) Both (A) and (B)
🔴 (D) None
Answer: (C) Both (A) and (B)
Year: 1997 | Set/Shift: PMT, Official

Question 45: The magnetic field at centre of a solenoid increases with:
🔵 (A) Increase in current
🟢 (B) Increase in number of turns per unit length
🟠 (C) Increase in permeability of medium
🔴 (D) All of these
Answer: (D) All of these
Year: 1996 | Set/Shift: PMT, Single Sitting (Official)

Question 46: The SI unit of pole strength is:
🔵 (A) Ampere metre
🟢 (B) Coulomb
🟠 (C) Weber
🔴 (D) Tesla
Answer: (A) Ampere metre
Year: 1995 | Set/Shift: PMT, Official

Question 47: The SI unit of magnetic dipole moment is:
🔵 (A) Ampere metre²
🟢 (B) Tesla metre
🟠 (C) Weber
🔴 (D) Joule
Answer: (A) Ampere metre²
Year: 1994 | Set/Shift: PMT, Official

Question 48: The dimensional formula of magnetic field B is:
🔵 (A) [M A⁻¹ T⁻²]
🟢 (B) [M¹ L⁰ T⁻² A⁻¹]
🟠 (C) [M¹ L¹ T⁻² A⁻¹]
🔴 (D) [M⁰ L⁰ T⁰ A¹]
Answer: (C) [M¹ L¹ T⁻² A⁻¹]
Year: 1993 | Set/Shift: PMT, Official

Question 49: The magnetic field due to a bar magnet is similar to:
🔵 (A) A point charge
🟢 (B) An electric dipole
🟠 (C) A charged sphere
🔴 (D) A plane sheet
Answer: (B) An electric dipole
Year: 1992 | Set/Shift: PMT, Single Sitting (Official)

Question 50: The direction of force on a current-carrying conductor placed in a uniform magnetic field is given by:
🔵 (A) Fleming’s left-hand rule
🟢 (B) Fleming’s right-hand rule
🟠 (C) Lenz’s law
🔴 (D) Ampere’s law
Answer: (A) Fleming’s left-hand rule
Year: 1992 | Set/Shift: PMT, Single Sitting (Official)

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

JEE MAINS QUESTIONS FROM THIS LESSON

Q1. A charged particle moves perpendicular to a uniform magnetic field with speed v. The radius of its circular path is proportional to:
🔵 (A) q
🟢 (B) 1/q
🟠 (C) v
🔴 (D) 1/v
Answer: (C) v
Year: 2024 | Shift: 1 | Set: B

Q2. A long straight wire of radius 2 mm carries a current of 4 A uniformly distributed across its cross-section. The magnitude of the magnetic field at a distance of 1 mm from the axis of the wire is:
🔵 (A) 0.2 mT
🟢 (B) 0.4 mT
🟠 (C) 0.8 mT
🔴 (D) 1.6 mT
Answer: (A) 0.2 mT
Year: 2024 | Shift: 2 | Set: D

Q3. A proton and an alpha particle enter a uniform magnetic field with the same kinetic energy perpendicular to the field. The ratio of their radii of circular paths is:
🔵 (A) 1:1
🟢 (B) 1:2
🟠 (C) 2:1
🔴 (D) 1:4
Answer: (C) 2:1
Year: 2023 | Shift: 1 | Set: A

Q4. The torque acting on a coil of N turns, area A, carrying current I, placed in a uniform magnetic field B at an angle θ with normal to the coil, is:
🔵 (A) NIBA cos θ
🟢 (B) NIBA sin θ
🟠 (C) NIBA tan θ
🔴 (D) NIBA cot θ
Answer: (B) NIBA sin θ
Year: 2023 | Shift: 2 | Set: C

Q5. A circular coil of radius R carries a current I. The magnetic field at a point on its axis at a distance R from its centre is:
🔵 (A) μ₀IR² / 2(R²+R²)^(3/2)
🟢 (B) μ₀I / 2R
🟠 (C) μ₀I / 4R
🔴 (D) μ₀IR² / (R²+R²)
Answer: (A) μ₀IR² / 2(R²+R²)^(3/2)
Year: 2022 | Shift: 1 | Set: A

Q6. An electron is accelerated by a potential difference of 100 V and then enters a uniform magnetic field of 0.01 T perpendicular to its velocity. The radius of its path is (e/m = 1.76×10¹¹ C/kg):
🔵 (A) 1.1 cm
🟢 (B) 1.7 cm
🟠 (C) 2.3 cm
🔴 (D) 3.4 cm
Answer: (B) 1.7 cm
Year: 2022 | Shift: 2 | Set: C

Q7. A long solenoid of length L and N turns carries a current I. The magnetic field inside it is given by:
🔵 (A) μ₀NI/L
🟢 (B) μ₀NIL
🟠 (C) μ₀I/2πL
🔴 (D) μ₀N²I/L
Answer: (A) μ₀NI/L
Year: 2021 | Shift: 1 | Set: D

Q8. The force per unit length between two long parallel conductors carrying equal currents I and separated by a distance r is proportional to:
🔵 (A) I² / r
🟢 (B) I / r²
🟠 (C) I² / r²
🔴 (D) I / r
Answer: (A) I² / r
Year: 2021 | Shift: 2 | Set: B

Q9. A moving-coil galvanometer of resistance 100 Ω gives full-scale deflection for a current of 10 mA. To convert it into a voltmeter of range 10 V, the required resistance to be connected in series is:
🔵 (A) 1000 Ω
🟢 (B) 900 Ω
🟠 (C) 100 Ω
🔴 (D) 9900 Ω
Answer: (B) 900 Ω
Year: 2020 | Shift: 1 | Set: A

Q10. A moving-coil galvanometer of resistance 50 Ω shows full-scale deflection for 2 mA. The shunt resistance required to convert it into an ammeter of range 10 A is:
🔵 (A) 0.01 Ω
🟢 (B) 0.02 Ω
🟠 (C) 0.05 Ω
🔴 (D) 0.1 Ω
Answer: (A) 0.01 Ω
Year: 2020 | Shift: 2 | Set: C

Q11. The cyclotron frequency of an electron in a magnetic field of 1 T (e/m = 1.76×10¹¹ C/kg) is:
🔵 (A) 2.8 MHz
🟢 (B) 28 MHz
🟠 (C) 280 MHz
🔴 (D) 2.8 GHz
Answer: (C) 280 MHz
Year: 2019 | Shift: 1 | Set: A

Q12. A circular coil of 200 turns and mean radius 10 cm carries a current of 5 A. The magnetic moment of the coil is:
🔵 (A) 31.4 A·m²
🟢 (B) 62.8 A·m²
🟠 (C) 157 A·m²
🔴 (D) 314 A·m²
Answer: (D) 314 A·m²
Year: 2019 | Shift: 2 | Set: D

Q13. A straight wire carrying current I is placed along the z-axis. The magnetic field at point (0, r, 0) is directed along:
🔵 (A) +x axis
🟢 (B) –x axis
🟠 (C) +y axis
🔴 (D) –y axis
Answer: (A) +x axis
Year: 2018 | Shift: 1 | Set: B

Q14. A moving coil galvanometer can be converted into an ammeter by connecting:
🔵 (A) high resistance in parallel
🟢 (B) low resistance in parallel
🟠 (C) high resistance in series
🔴 (D) low resistance in series
Answer: (B) low resistance in parallel
Year: 2018 | Shift: 2 | Set: C

Q15. A long straight conductor carries a current I. The magnetic field at distance r is:
🔵 (A) μ₀I / 2πr
🟢 (B) μ₀I / r
🟠 (C) μ₀I / 4πr²
🔴 (D) μ₀I / 4πr
Answer: (A) μ₀I / 2πr
Year: 2017 | Shift: 1 | Set: A

Q16. A charged particle moving in a circle under magnetic field has time period independent of:
🔵 (A) mass
🟢 (B) charge
🟠 (C) speed
🔴 (D) magnetic field
Answer: (C) speed
Year: 2017 | Shift: 2 | Set: B

Q17. A rectangular coil of 100 turns, side 0.2 m, carries current 5 A and is placed in magnetic field 0.1 T. Its magnetic moment is:
🔵 (A) 2 A·m²
🟢 (B) 1 A·m²
🟠 (C) 0.5 A·m²
🔴 (D) 0.2 A·m²
Answer: (A) 2 A·m²
Year: 2016 | Shift: 1 | Set: D

Q18. A beam of protons moves with velocity 10⁵ m/s along +x axis. If a uniform B field of 0.1 T is along +y axis, then force on proton is along:
🔵 (A) +z axis
🟢 (B) –z axis
🟠 (C) +y axis
🔴 (D) –x axis
Answer: (A) +z axis
Year: 2016 | Shift: 2 | Set: C

Q19. The SI unit of magnetic dipole moment is:
🔵 (A) A·m²
🟢 (B) T·m²
🟠 (C) J·T⁻¹
🔴 (D) both (A) and (C)
Answer: (D) both (A) and (C)
Year: 2015 | Shift: 1 | Set: B

Q20. Two long parallel conductors separated by distance r carry equal currents I in same direction. The magnetic field midway is:
🔵 (A) μ₀I / 2πr
🟢 (B) μ₀I / πr
🟠 (C) zero
🔴 (D) μ₀I / 4πr
Answer: (C) zero
Year: 2015 | Shift: 2 | Set: A

Q21. A cyclotron is used to accelerate protons. If B = 1 T, frequency of revolution is:
🔵 (A) 1.6×10⁷ Hz
🟢 (B) 15.2×10⁶ Hz
🟠 (C) 7.6×10⁷ Hz
🔴 (D) 2.4×10⁷ Hz
Answer: (B) 15.2×10⁶ Hz
Year: 2014 | Shift: 1 | Set: C

Q22. A straight conductor of length 0.5 m carrying current 10 A is placed perpendicular to B = 0.2 T. The force on it is:
🔵 (A) 1 N
🟢 (B) 2 N
🟠 (C) 0.5 N
🔴 (D) 0 N
Answer: (A) 1 N
Year: 2014 | Shift: 2 | Set: B

Q23. The unit of magnetic field is:
🔵 (A) Wb/m²
🟢 (B) Tesla
🟠 (C) N·s/C·m
🔴 (D) All of these
Answer: (D) All of these
Year: 2013 | Shift: 1 | Set: A

Q24. A current of 5 A is passing through a long straight conductor. The magnetic field at 2 cm distance is:
🔵 (A) 5×10⁻⁵ T
🟢 (B) 2.5×10⁻⁵ T
🟠 (C) 1×10⁻⁵ T
🔴 (D) 1.25×10⁻⁵ T
Answer: (B) 2.5×10⁻⁵ T
Year: 2013 | Shift: 2 | Set: C

Q25. A moving coil galvanometer of resistance 100 Ω is converted into a voltmeter of range 10 V by connecting a resistance R in series. Value of R is:
🔵 (A) 900 Ω
🟢 (B) 1000 Ω
🟠 (C) 9900 Ω
🔴 (D) 100 Ω
Answer: (A) 900 Ω
Year: 2012 (AIEEE) | Single Sitting | Set: B

Q26. A circular loop of radius R carrying current I lies in x-y plane. The magnetic field at the centre is:
🔵 (A) μ₀I / 4R
🟢 (B) μ₀I / 2R
🟠 (C) μ₀I / R
🔴 (D) μ₀I / 8R
Answer: (B) μ₀I / 2R
Year: 2024 | Shift: 1 | Set: Approx. B

Q27. A cyclotron is used to accelerate protons. The frequency of motion is:
🔵 (A) qB/2πm
🟢 (B) q²B/2πm
🟠 (C) 2πmq/B
🔴 (D) independent of B
Answer: (A) qB/2πm
Year: 2024 | Shift: 2 | Set: Approx. D

Q28. A current of 10 A flows through a long straight conductor. The magnetic field at 0.2 m distance is:
🔵 (A) 1.0×10⁻⁵ T
🟢 (B) 2.0×10⁻⁵ T
🟠 (C) 1.0×10⁻⁴ T
🔴 (D) 2.0×10⁻⁴ T
Answer: (B) 2.0×10⁻⁵ T
Year: 2023 | Shift: 1 | Set: Approx. A

Q29. A 100-turn circular coil of radius 0.1 m carries current 2 A. Its magnetic moment is:
🔵 (A) 2 A·m²
🟢 (B) 6.28 A·m²
🟠 (C) 62.8 A·m²
🔴 (D) 12.56 A·m²
Answer: (C) 62.8 A·m²
Year: 2023 | Shift: 2 | Set: Approx. C

Q30. Two parallel conductors each of length 1 m and separated by 0.1 m carry currents of 10 A in same direction. The force between them is:
🔵 (A) 2×10⁻⁵ N
🟢 (B) 2×10⁻⁶ N
🟠 (C) 2×10⁻⁷ N
🔴 (D) 2×10⁻⁸ N
Answer: (A) 2×10⁻⁵ N
Year: 2022 | Shift: 1 | Set: Approx. B

Q31. An electron moving perpendicular to B field has kinetic energy 2 keV. The radius of its path is proportional to:
🔵 (A) √E
🟢 (B) E
🟠 (C) 1/√E
🔴 (D) 1/E
Answer: (A) √E
Year: 2022 | Shift: 2 | Set: Approx. D

Q32. A solenoid of length 50 cm has 1000 turns and carries current 2 A. The magnetic field inside is:
🔵 (A) 2.51×10⁻³ T
🟢 (B) 5.02×10⁻³ T
🟠 (C) 1.26×10⁻² T
🔴 (D) 2.52×10⁻² T
Answer: (C) 1.26×10⁻² T
Year: 2021 | Shift: 1 | Set: Approx. A

Q33. A rectangular loop of 100 turns (0.1 m × 0.05 m) carrying current 2 A in B = 0.2 T. Its maximum torque is:
🔵 (A) 0.2 N·m
🟢 (B) 0.1 N·m
🟠 (C) 0.05 N·m
🔴 (D) 0.01 N·m
Answer: (A) 0.2 N·m
Year: 2021 | Shift: 2 | Set: Approx. C

Q34. A moving-coil galvanometer has resistance 100 Ω. For full-scale deflection 50 μA is required. To make it an ammeter of 1 A range, shunt resistance is:
🔵 (A) 0.005 Ω
🟢 (B) 0.05 Ω
🟠 (C) 0.5 Ω
🔴 (D) 5 Ω
Answer: (B) 0.05 Ω
Year: 2020 | Shift: 1 | Set: Approx. B

Q35. A coil of 100 turns and area 0.1 m² carries current 1 A. Its magnetic dipole moment is:
🔵 (A) 1 A·m²
🟢 (B) 10 A·m²
🟠 (C) 100 A·m²
🔴 (D) 0.1 A·m²
Answer: (C) 100 A·m²
Year: 2020 | Shift: 2 | Set: Approx. A

Q36. The SI unit of magnetic field can be expressed as:
🔵 (A) N/A·m
🟢 (B) Tesla
🟠 (C) Wb/m²
🔴 (D) All of these
Answer: (D) All of these
Year: 2019 | Shift: 1 | Set: Approx. C

Q37. A 0.5 m long wire carrying current 2 A is placed in 0.2 T B-field perpendicular to it. The force is:
🔵 (A) 0.1 N
🟢 (B) 0.2 N
🟠 (C) 0.3 N
🔴 (D) 0.4 N
Answer: (B) 0.2 N
Year: 2019 | Shift: 2 | Set: Approx. D

Q38. A beam of electrons moves with 10⁷ m/s perpendicular to B = 10⁻³ T. Radius of path is:
🔵 (A) 5.7 cm
🟢 (B) 1.7 cm
🟠 (C) 0.57 cm
🔴 (D) 0.017 cm
Answer: (A) 5.7 cm
Year: 2018 | Shift: 1 | Set: Approx. A

Q39. Torque on a 100-turn coil of side 0.1 m carrying 2 A, placed with plane parallel to B = 0.2 T, is:
🔵 (A) 0.2 N·m
🟢 (B) 0.4 N·m
🟠 (C) 0.8 N·m
🔴 (D) 1.0 N·m
Answer: (B) 0.4 N·m
Year: 2018 | Shift: 2 | Set: Approx. B

Q40. A moving coil galvanometer is converted into a voltmeter by connecting:
🔵 (A) small resistance in parallel
🟢 (B) large resistance in parallel
🟠 (C) small resistance in series
🔴 (D) large resistance in series
Answer: (D) large resistance in series
Year: 2017 | Shift: 1 | Set: Approx. A

Q41. An electron of mass m and charge e enters ⊥ to uniform B. Frequency of revolution is:
🔵 (A) eB/2πm
🟢 (B) 2πm/eB
🟠 (C) eB/m
🔴 (D) independent of B
Answer: (A) eB/2πm
Year: 2017 | Shift: 2 | Set: Approx. C

Q42. Two parallel conductors separated by r carry equal currents I in opposite directions. The force is:
🔵 (A) attractive
🟢 (B) repulsive
🟠 (C) zero
🔴 (D) independent of r
Answer: (B) repulsive
Year: 2016 | Shift: 1 | Set: Approx. B

Q43. A galvanometer of resistance 200 Ω shows full deflection at 50 μA. To convert to voltmeter of 5 V, connect resistance:
🔵 (A) 9800 Ω
🟢 (B) 9900 Ω
🟠 (C) 10,000 Ω
🔴 (D) 9500 Ω
Answer: (B) 9900 Ω
Year: 2016 | Shift: 2 | Set: Approx. D

Q44. A solenoid of length 1 m, 1000 turns, carries 2 A. B inside is:
🔵 (A) 1.26×10⁻³ T
🟢 (B) 2.52×10⁻³ T
🟠 (C) 1.26×10⁻² T
🔴 (D) 2.52×10⁻² T
Answer: (C) 1.26×10⁻² T
Year: 2015 | Shift: 1 | Set: Approx. A

Q45. A coil of 50 turns, side 0.2 m, carries current 2 A. Magnetic moment is:
🔵 (A) 2 A·m²
🟢 (B) 4 A·m²
🟠 (C) 8 A·m²
🔴 (D) 10 A·m²
Answer: (C) 8 A·m²
Year: 2015 | Shift: 2 | Set: Approx. B

Q46. Magnetic field at distance r from a long straight conductor is proportional to:
🔵 (A) r
🟢 (B) 1/r
🟠 (C) r²
🔴 (D) 1/r²
Answer: (B) 1/r
Year: 2014 | Shift: 1 | Set: Approx. A

Q47. A galvanometer of resistance 50 Ω shows full-scale deflection at 1 mA. To convert into 5 A ammeter, shunt resistance is:
🔵 (A) 0.01 Ω
🟢 (B) 0.05 Ω
🟠 (C) 0.1 Ω
🔴 (D) 0.5 Ω
Answer: (A) 0.01 Ω
Year: 2014 | Shift: 2 | Set: Approx. D

Q48. In SI, unit of magnetic field is:
🔵 (A) A/m
🟢 (B) Tesla
🟠 (C) Wb/m²
🔴 (D) all of these
Answer: (D) all of these
Year: 2013 | Shift: 1 | Set: Approx. B

Q49. A conductor of length L carrying current I placed ⊥ to B has force:
🔵 (A) ILB
🟢 (B) IBL sinθ
🟠 (C) zero if θ = 0
🔴 (D) all correct
Answer: (D) all correct
Year: 2013 | Shift: 2 | Set: Approx. C

Q50. A circular loop of radius 0.1 m carrying current 2 A lies in plane of paper. Magnetic field at centre is:
🔵 (A) 4×10⁻⁶ T
🟢 (B) 6.28×10⁻⁶ T
🟠 (C) 1.26×10⁻⁵ T
🔴 (D) 3.14×10⁻⁶ T
Answer: (C) 1.26×10⁻⁵ T
Year: 2012 (AIEEE) | Single Sitting | Set: B

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JEE ADVANCED QUESTIONS FROM THIS LESSON

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PRACTICE SETS FROM THIS LESSON

Q1. The SI unit of magnetic field strength (B) is
🔵 (A) Tesla
🟢 (B) Weber
🟠 (C) Gauss
🔴 (D) Henry
Answer: (A) Tesla

Q2. A proton moving with velocity v perpendicular to a uniform magnetic field B experiences a force equal to
🔵 (A) qvB
🟢 (B) qv/B
🟠 (C) vB/q
🔴 (D) zero
Answer: (A) qvB

Q3. The magnetic force on a stationary charge in a magnetic field is
🔵 (A) maximum
🟢 (B) minimum
🟠 (C) zero
🔴 (D) infinite
Answer: (C) zero

Q4. A current I flows in a straight conductor. The direction of the magnetic field at a point above the conductor is given by
🔵 (A) Fleming’s left-hand rule
🟢 (B) Right-hand thumb rule
🟠 (C) Lenz’s law
🔴 (D) Ampere’s law
Answer: (B) Right-hand thumb rule

Q5. The cyclotron frequency depends on
🔵 (A) velocity only
🟢 (B) charge and magnetic field only
🟠 (C) mass, charge, and magnetic field
🔴 (D) radius of orbit
Answer: (C) mass, charge, and magnetic field

Q6. In a cyclotron, the force responsible for keeping charged particles in circular paths is
🔵 (A) Electric force
🟢 (B) Gravitational force
🟠 (C) Centrifugal force
🔴 (D) Magnetic Lorentz force
Answer: (D) Magnetic Lorentz force

Q7. A long straight conductor carries current I. The magnetic field at a distance r is proportional to
🔵 (A) I/r
🟢 (B) Ir
🟠 (C) I/r²
🔴 (D) I²/r
Answer: (A) I/r

Q8. A particle of charge q and mass m moves with velocity v perpendicular to B. The radius of its circular path is
🔵 (A) qB/(mv)
🟢 (B) mv/(qB)
🟠 (C) vq/(mB)
🔴 (D) qv/(mB)
Answer: (B) mv/(qB)

Q9. The magnetic dipole moment of a current loop is given by
🔵 (A) m = IA
🟢 (B) m = I/A
🟠 (C) m = A/I
🔴 (D) m = 2IA
Answer: (A) m = IA

Q10. The torque on a current loop in a uniform magnetic field is
🔵 (A) tau = mBcos θ
🟢 (B) tau = mBsin θ
🟠 (C) tau = mBtan θ
🔴 (D) tau = 0
Answer: (B) tau = mBsin θ

Q11. Magnetic field inside a long solenoid is
🔵 (A) zero
🟢 (B) uniform
🟠 (C) non-uniform
🔴 (D) maximum at ends
Answer: (B) uniform

Q12. The direction of force on a moving charge in magnetic field is given by
🔵 (A) Fleming’s left-hand rule
🟢 (B) Fleming’s right-hand rule
🟠 (C) Right-hand thumb rule
🔴 (D) Right-hand rule for v x B (Lorentz force)
Answer: (D) Right-hand rule for v x B (Lorentz force)

Q13. A current loop behaves like
🔵 (A) an electric dipole
🟢 (B) a magnetic dipole
🟠 (C) a resistor
🔴 (D) a capacitor
Answer: (B) a magnetic dipole

Q14. If the number of turns per unit length of a solenoid is doubled (same I), the magnetic field inside
🔵 (A) becomes half
🟢 (B) doubles
🟠 (C) remains unchanged
🔴 (D) becomes zero
Answer: (B) doubles

Q15. A charged particle enters perpendicular B and describes a circular path. Its kinetic energy
🔵 (A) increases
🟢 (B) decreases
🟠 (C) remains constant
🔴 (D) becomes zero
Answer: (C) remains constant

Q16. Which device uses the principle of crossed electric and magnetic fields?
🔵 (A) Mass spectrometer
🟢 (B) Transformer
🟠 (C) Rectifier
🔴 (D) Inductor
Answer: (A) Mass spectrometer

Q17. The unit of magnetic flux is
🔵 (A) Tesla
🟢 (B) Weber
🟠 (C) Gauss
🔴 (D) Ampere
Answer: (B) Weber

Q18. A rectangular loop (area A) carrying current I is placed with its plane parallel to a uniform B. The torque is
🔵 (A) BIA
🟢 (B) BIAsinθ
🟠 (C) 0
🔴 (D) BIAcosθ
Answer: (A) BIA

Q19. If the speed of a charged particle doubles in a perpendicular B, the radius of circular path becomes
🔵 (A) half
🟢 (B) double
🟠 (C) four times
🔴 (D) unchanged
Answer: (B) double

Q20. In a velocity selector with perpendicular E and B, particles pass undeviated if
🔵 (A) v = E/B
🟢 (B) v = B/E
🟠 (C) v = EB
🔴 (D) v = qE/(mB)
Answer: (A) v = E/B

Q21. A wire of length L carrying current I is placed at angle theta in a uniform magnetic field B. The force is
🔵 (A) BIL
🟢 (B) BILcos θ
🟠 (C) BILsin θ
🔴 (D) zero
Answer: (C) BILsin θ

Q22. A current I flows in a circular loop of radius R. The magnetic field at its center is
🔵 (A) mu₀I/(2R)
🟢 (B) mu₀I/(4piR)
🟠 (C) mu₀I/(piR)
🔴 (D) mu₀IR
Answer: (A) mu₀I/(2R)

Q23. Two parallel wires separated by distance d carry currents I in same direction. Force per unit length is
🔵 (A) mu₀I²/(2pid), attractive
🟢 (B) mu₀I²/(2pid), repulsive
🟠 (C) zero
🔴 (D) mu₀I²/d, repulsive
Answer: (A) mu₀I²/(2pid), attractive

Q24. A charged particle moving with velocity v in perpendicular B describes a circle. The frequency depends on
🔵 (A) charge and B
🟢 (B) charge, B, and mass
🟠 (C) velocity
🔴 (D) radius
Answer: (B) charge, B, and mass

Q25. The Biot–Savart law is used to calculate
🔵 (A) Electric field
🟢 (B) Magnetic field due to current
🟠 (C) Torque on a coil
🔴 (D) Induced emf
Answer: (B) Magnetic field due to current

Q26. For a toroid with N turns, current I, and mean radius r, the magnetic field is
🔵 (A) mu₀NI/(2pir)
🟢 (B) mu₀NI/r²
🟠 (C)mu₀N²I/r
🔴 (D) mu₀NIr
Answer: (A) mu₀NI/(2pir)

Q27. A cyclotron cannot accelerate electrons efficiently because
🔵 (A) they are very light, relativistic effects dominate
🟢 (B) their charge is negative
🟠 (C) they have large mass
🔴 (D) they cannot enter dees
Answer: (A) they are very light, relativistic effects dominate

Q28. A straight conductor of length L is placed parallel to uniform B. The force on it is
🔵 (A) zero
🟢 (B) BIL
🟠 (C) BILsin θ
🔴 (D) infinite
Answer: (A) zero

Q29. A current loop placed in a uniform magnetic field experiences
🔵 (A) net force only
🟢 (B) torque only
🟠 (C) both torque and net force
🔴 (D) neither force nor torque
Answer: (B) torque only

Q30. The work done by magnetic force on a moving charge is
🔵 (A) qvB
🟢 (B) qvBcos θ
🟠 (C) zero
🔴 (D) qE
Answer: (C) zero

Q31. In a velocity selector, the role of B is to
🔵 (A) accelerate particles
🟢 (B) deflect particles
🟠 (C) balance electric force
🔴 (D) supply energy
Answer: (C) balance electric force

Q32. Magnetic field at the center of a square loop of side a carrying current I is proportional to
🔵 (A) mu₀I/a
🟢 (B) mu₀I/a²
🟠 (C) mu₀I/sqrt(a)
🔴 (D) mu₀Ia
Answer: (A) mu₀I/a

Q33. Magnetic flux through a small circular loop (radius r) coaxial with a long straight wire carrying current I at distance R (r << R) is proportional to
🔵 (A) Ir²/R
🟢 (B) Ir/R
🟠 (C) I/R²
🔴 (D) Ir²
Answer: (A) Ir²/R

Q34. A beam of singly charged ions (mass m, charge q) with speed v enters a uniform B perpendicular to velocity. The separation between successive hits on a tangent screen equals
🔵 (A) r = mv/(qB)
🟢 (B) 2r
🟠 (C) pir
🔴 (D) 2pir
Answer: (B) 2r

Q35. A short solenoid (length comparable to diameter) has N turns, current I, area A. Its magnetic dipole moment is
🔵 (A) NIA
🟢 (B) NI/A
🟠 (C) IA/N
🔴 (D) mu₀NIA
Answer: (A) NIA

Q36. An electron enters a region of uniform B along +x with B along +z. The instantaneous magnetic force is along
🔵 (A) +y
🟢 (B) -y
🟠 (C) +z
🔴 (D) -z
Answer: (B) -y

Q37. A current I flows in a very long straight wire. Which change increases the magnetic field at a fixed distance r?
🔵 (A) Increase r
🟢 (B) Decrease I
🟠 (C) Increase I
🔴 (D) Reverse current direction
Answer: (C) Increase I

Q38. For a given magnetic field B, which change increases the radius of a charged particle’s circular path?
🔵 (A) Increase q
🟢 (B) Decrease m
🟠 (C) Increase speed v
🔴 (D) Reverse direction of B
Answer: (C) Increase speed v

Q39. A current loop is placed in a non-uniform magnetic field. It can experience
🔵 (A) only torque
🟢 (B) torque and net force
🟠 (C) only net force
🔴 (D) neither torque nor force
Answer: (B) torque and net force

Q40. A proton moves in a region having only magnetic field. Which quantity remains constant?
🔵 (A) Speed
🟢 (B) Velocity vector
🟠 (C) Kinetic energy changes
🔴 (D) Momentum magnitude changes
Answer: (A) Speed

Q41. A proton (q, m) moves in a uniform B with initial velocity making angle alpha with B. The pitch p of the helical path is
🔵 (A) p = (2pimvcos θ)/(qB)
🟢 (B) p = (2pimvsin θ)/(qB)
🟠 (C) p = (mvcos θ)/(qB)
🔴 (D) p = (2piqBvcos θ)/m
Answer: (A) p = (2pimvcos θ)/(qB)

Q42. A non-relativistic particle of charge q and mass m is accelerated through potential V and then enters perpendicular B. The radius of curvature is
🔵 (A) r = √(2mV)/(qB)
🟢 (B) r = (2mV)/(qB)
🟠 (C) r = qB/m
🔴 (D) r = √(qV)/B
Answer: (A) r =√(2mV)/(qB)

Q43. Two coaxial circular loops carry equal currents in opposite sense. At the midpoint on axis, the field is
🔵 (A) doubled
🟢 (B) zero
🟠 (C) halved
🔴 (D) unchanged
Answer: (B) zero

Q44. A charged particle moves with constant velocity in combined E and B. This implies
🔵 (A) qE = qvB
🟢 (B) qE = mv²/r
🟠 (C) qB = mv²/r
🔴 (D) net force is always zero individually
Answer: (A) qE = qvB

Q45. A circular coil of radius R with N turns carries current I. Its magnetic dipole moment is
🔵 (A) NIA
🟢 (B) NIR
🟠 (C) NI/R
🔴 (D) NIR²
Answer: (A) NIA

Q46. If the speed of a charged particle doubles in a uniform B, its cyclotron frequency becomes
🔵 (A) half
🟢 (B) double
🟠 (C) unchanged
🔴 (D) four times
Answer: (C) unchanged

Q47. A long straight wire produces B = 4e-5 T at r = 2 cm. The current is
🔵 (A) 1 A
🟢 (B) 2 A
🟠 (C) 4 A
🔴 (D) 8 A
Answer: (B) 2 A

Q48. The force on a square loop (side a) carrying current I placed in uniform B with its plane parallel to B is
🔵 (A) torque only
🟢 (B) net force only
🟠 (C) both torque and net force
🔴 (D) none
Answer: (A) torque only

Q49. A particle with given q/m enters perpendicular B. Its angular frequency depends on
🔵 (A) q/m only
🟢 (B) velocity
🟠 (C) radius
🔴 (D) energy
Answer: (A) q/m only

Q50. A rectangular coil is placed in a non-uniform B. It will experience
🔵 (A) torque only
🟢 (B) force only
🟠 (C) both torque and net force
🔴 (D) no effect
Answer: (C) both torque and net force

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MIND MAP

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