100 High-Scoring MCQs on Electromagnetism: Set-2 From Basics to Expert Level

100 High-Scoring MCQs on Electromagnetism: Set-2 From Basics to Expert Level

⚡ Master "Electromagnetism" with 100 MCQs (Set - 2) ⚡  

⚡ From Basic to Expert Level! ⚡


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Are you preparing for exams or aiming to strengthen your understanding of Physics – Electromagnetism? Looking for a complete set of 100 high-quality MCQs from basic to expert level to sharpen your concepts and boost exam confidence?

This carefully curated collection of Multiple Choice Questions (MCQs) covers all major topics of the unit, including:

• Magnetic Field
• Force on a Current Carrying Conductor
• Magnetic Flux
• Ampere’s Law
• Magnetic Field due to a Solenoid
• Applications of Magnetic Field
• Motion of a Charged Particle in Uniform Magnetic Field
• Determination of e/m for an Electron
• Velocity Selector
• Torque on a Current Carrying Loop / Coil
• MRI (Magnetic Resonance Imaging)
• Galvanometer and its Conversions (Ammeter & Voltmeter)
• Avometer / Multimeter
• Current, Voltage & Resistance Measurement
• Digital Multimeters

Each MCQ is provided with a clear solution or explanation, helping you:

  • understand concepts step-by-step
  • improve numerical problem-solving skills
  • revise quickly before exams
  • build strong conceptual clarity

Whether you’re revising for school exams, board exams, or entry tests, this comprehensive MCQ set is designed to take your preparation to the next level.

💡 Study Tip: Start with basic questions, move to intermediate, and finally challenge yourself with expert-level MCQs for maximum learning.

 What you’ll get:

Set-1: Basic Level – Perfect for beginners, focusing on fundamentals like Magnetic Field, Magnetic Flux, and Force on Current Carrying Conductor.

Set-2: Intermediate Level – Strengthens application skills with Ampere’s Law, Solenoids, Motion of Charged Particles, and Velocity Selector.

Set-3: Advanced Level – Develops deeper understanding through Torque on Coil, e/m of Electron, Galvanometer Conversions, and Measuring Instruments.

Set-4: Expert Level – High-level conceptual and numerical MCQs covering the entire Electromagnetism unit, designed to test speed, accuracy, and critical thinking.

Electromagnetism MCQs (Set-1: Basic Level

MCQs No. 1–25 (Basic Concepts)

MCQ No. 1
The force on a moving charge in a magnetic field is maximum when:
a. Velocity is parallel to magnetic field
b. Velocity is perpendicular to magnetic field
c. Velocity is at 45° to magnetic field
d. Velocity is zero

Correct answer: b. Velocity is perpendicular to magnetic field
Explanation: Magnetic force F=qvBsin⁡θF = qvB \sin\theta is maximum when θ = 90°.

MCQ No. 2
The energy stored in an inductor carrying current I is:
a. ½ LI²
b. LI²
c. ½ L²I
d. L/2

Correct answer: a. ½ LI²
Explanation: Magnetic energy stored in the inductor is U=12LI2U = \frac{1}{2}LI^2 .

MCQ No. 3
A charged particle moves in a uniform magnetic field in a circle. Its speed:
a. Increases
b. Decreases
c. Remains constant
d. Becomes zero

Correct answer: c. Remains constant
Explanation: Magnetic force acts perpendicular to velocity; it changes direction only.

MCQ No. 4
Magnetic field at the center of a circular loop of radius R carrying current I:
a. μ0I2πR\frac{\mu_0 I}{2 \pi R}

b. μ0I2R\frac{\mu_0 I}{2 R}

c. μ0I4πR2\frac{\mu_0 I}{4 \pi R^2}

d. μ0IR\frac{\mu_0 I}{R}

Correct answer: b. μ0I2R\frac{\mu_0 I}{2 R}

Explanation: Derived from Biot–Savart law for circular loop.

MCQ No. 5
Torque on a magnetic dipole along uniform magnetic field:
a. Maximum
b. Zero
c. Half maximum
d. Depends on dipole moment

Correct answer: b. Zero
Explanation: τ=μBsin⁡θ\tau = \mu B \sin\theta, θ = 0 ⇒ τ = 0.

MCQ No. 6
Faraday’s law gives induced EMF:
a. NdΦdtN \frac{d\Phi}{dt}

b. −NdΦdt-N \frac{d\Phi}{dt}

c. ΦN\frac{\Phi}{N}

d. NΦ2N\Phi^2

Correct answer: b. −NdΦdt-N \frac{d\Phi}{dt}

Explanation: Negative sign = Lenz’s law (opposes change).

MCQ No. 7
Displacement current is introduced to:
a. Explain current in superconductors
b. Correct Ampere’s law for time-varying fields
c. Define magnetic field in solenoid
d. Measure EM waves

Correct answer: b. Correct Ampere’s law for time-varying fields
Explanation: Ensures continuity of current in changing electric fields.

MCQ No. 8
Velocity component along magnetic field in helical motion:
a. Changes
b. Remains constant
c. Becomes zero
d. Oscillates

Correct answer: b. Remains constant
Explanation: Force acts perpendicular; parallel component unaffected.

MCQ No. 9
SI unit of inductance:
a. Henry (H)
b. Tesla (T)
c. Weber (Wb)
d. Ampere (A)

Correct answer: a. Henry (H)
Explanation: 1 H = 1 Wb/A.

MCQ No. 10
Energy density of magnetic field:
a. B22μ0\frac{B^2}{2\mu_0}

b. μ0B22\frac{\mu_0 B^2}{2}

c. B2μ0\frac{B^2}{\mu_0}

d. μ₀B²

Correct answer: a. B22μ0\frac{B^2}{2\mu_0}
Explanation: Energy per unit volume: u = B² / 2μ₀.

MCQ No. 11
Cyclotron frequency of a particle:
a. qB / m
b. qB / (2πm)
c. m / qB
d. B / q

Correct answer: b. qB / (2πm)
Explanation: f = qB / 2πm.

MCQ No. 12
Magnetic flux through a surface depends on:
a. Area of surface
b. Magnetic field strength
c. Angle between B and normal
d. All above

Correct answer: d. All above
Explanation: Φ=BAcos⁡θ\Phi = B A \cos\theta .

MCQ No. 13
SI unit of magnetic flux:
a. Tesla
b. Weber
c. Henry
d. Coulomb

Correct answer: b. Weber (Wb)
Explanation: 1 Wb = 1 T·m².

MCQ No. 14
Magnetic field inside a long solenoid:
a. μ₀ n I
b. μ₀ I / 2R
c. μ₀ I n²
d. μ₀ I / L

Correct answer: a. μ₀ n I
Explanation: n = turns per unit length.

MCQ No. 15
A straight conductor experiences maximum force when:
a. Parallel to B
b. Perpendicular to B
c. Zero angle
d. Along current

Correct answer: b. Perpendicular to B
Explanation: F = I L × B, maximum at 90°.

MCQ No. 16
In an L-R circuit, current rises exponentially:
a. Instantaneously
b. Gradually
c. Linearly
d. Decreases

Correct answer: b. Gradually
Explanation: I(t) = (V/R)(1 – e^(–Rt/L)).

MCQ No. 17
Magnetic moment of a current loop:
a. I × area
b. I / area
c. B × area
d. I × B

Correct answer: a. I × area
Explanation: μ = I A (vector perpendicular to loop).

MCQ No. 18
EM waves are:
a. Longitudinal
b. Transverse
c. Both
d. None

Correct answer: b. Transverse
Explanation: E ⊥ B ⊥ direction of propagation.

MCQ No. 19
Energy of magnetic dipole in uniform B:
a. –μ · B
b. μB sin θ
c. μB cos θ
d. Zero

Correct answer: a. –μ · B
Explanation: U = –μB cosθ.

MCQ No. 20
Unit of magnetic field (B) in SI:
a. Tesla
b. Weber
c. Henry
d. Ampere

Correct answer: a. Tesla
Explanation: 1 T = 1 Wb/m².

MCQ No. 21
Magnetic field due to a long straight wire at distance r:
a. μ₀ I / (2π r)
b. μ₀ I / (4π r²)
c. μ₀ I / r
d. μ₀ I / (2 r²)

Correct answer: a. μ₀ I / (2π r)
Explanation: Biot–Savart law for long straight wire.

MCQ No. 22
Time constant of an LR circuit:
a. L / R
b. R / L
c. L × R
d. 1 / (LR)

Correct answer: a. L / R
Explanation: τ = L / R (time to reach 63% current).

MCQ No. 23
Direction of induced current opposes change in flux:
a. Lenz’s law
b. Faraday’s law
c. Ampere’s law
d. Biot-Savart law

Correct answer: a. Lenz’s law
Explanation: Ensures conservation of energy.

MCQ No. 24
Self-inductance of a solenoid depends on:
a. Number of turns
b. Cross-sectional area
c. Length of solenoid
d. All above

Correct answer: d. All above
Explanation: L = μ₀ n² A l.

MCQ No. 25
Mutual inductance depends on:
a. Geometry of coils
b. Number of turns
c. Magnetic coupling
d. All above

Correct answer: d. All above
Explanation: M = k√(L₁L₂), k = coupling coefficient.

Electromagnetism MCQs (Set-2: Intermediate Level, Q26–50)

MCQ No. 26
A proton moves perpendicular to a uniform magnetic field of 0.5 T with velocity 2 × 10⁶ m/s. Its radius of circular path is:
a. 0.05 m
b. 0.1 m
c. 0.2 m
d. 0.5 m

Correct answer: c. 0.2 m

Explanation: r=mvqB=1.67×10−27×2×1061.6×10−19×0.5≈0.2 mr = \frac{mv}{qB} = \frac{1.67 \times 10^{-27} \times 2 \times 10^6}{1.6 \times 10^{-19} \times 0.5} ≈ 0.2 \, m.

MCQ No. 27
The magnetic field at a point on the axis of a circular current loop:
a. Zero
b. Maximum at center
c. Maximum at infinite distance
d. Independent of radius

Correct answer: b. Maximum at centre
Explanation: B = μ₀I R² / [2(R² + x²)^(3/2)], max at x = 0.

MCQ No. 28
Two coils have self-inductances L₁ = 4 H and L₂ = 9 H, mutual inductance M = 6 H. Maximum possible coupling coefficient k =
a. 0.5
b. 0.8
c. 1
d. 0.9

Correct answer: b. 0.8

Explanation: k=ML1L2=6/36=0.8k = \frac{M}{\sqrt{L_1 L_2}} = 6 / \sqrt{36} = 0.8

MCQ No. 29
A circular loop of wire is rotated in a uniform magnetic field. Maximum EMF induced occurs when:
a. Plane of loop parallel to B
b. Plane of loop perpendicular to B
c. Loop stationary
d. None

Correct answer: a. Plane parallel to B
Explanation: ε = –N dΦ/dt, max rate of change occurs when loop plane is parallel to B.

MCQ No. 30
The magnetic field inside a toroid is:
a. Zero everywhere
b. μ₀ n I / (2π r)
c. μ₀ n I
d. μ₀ I / r²

Correct answer: b. μ₀ n I / (2π r)
Explanation: Toroid field derived from Ampere’s law: B = μ₀ n I / (2π r).

MCQ No. 31
If the radius of a circular loop is doubled, its magnetic moment (μ = IA) becomes:
a. Half
b. Double
c. Four times
d. Unchanged

Correct answer: c. Four times
Explanation: μ = I × A, A ∝ r² → μ ∝ r².

MCQ No. 32
In an RL circuit, after a long time:
a. Current = 0
b. Current = V/R
c. Voltage across L = V
d. Voltage across R = 0

Correct answer: b. Current = V/R
Explanation: Inductor behaves as short circuit at steady state.

MCQ No. 33
The force between two parallel currents I₁ and I₂ separated by distance d is:
a. F = μ₀ I₁ I₂ / (2π d)
b. F = μ₀ I₁ I₂ / d²
c. F = μ₀ I₁ I₂ / (4π d²)
d. F = μ₀ I₁ I₂ d

Correct answer: a. F = μ₀ I₁ I₂ / (2π d)
Explanation: Force per unit length between parallel currents: F/L=μ0I1I2/2πdF/L = μ₀ I₁ I₂ / 2π d.

MCQ No. 34
A wire carries 5 A in a magnetic field 0.2 T. Length perpendicular to B is 0.5 m. Force on wire:
a. 0.5 N
b. 0.25 N
c. 1 N
d. 2 N

Correct answer: b. 0.5 ×? Let’s calculate:
F = I L B = 5 × 0.5 × 0.2 = 0.5 N ✅

Correct answer: a. 0.5 N

MCQ No. 35
Magnetic field due to a long straight wire at 10 cm distance carrying 2 A:
a. 4 ×10⁻⁶ T
b. 2 ×10⁻⁵ T
c. 1 ×10⁻⁵ T
d. 2 ×10⁻⁶ T

Correct answer: c. 4 × 10⁻⁶ T
Explanation: B = μ₀ I / 2π r = (4π×10⁻⁷ × 2)/(2π ×0.1) ≈ 4×10⁻⁶ T.

MCQ No. 36
Energy stored in a magnetic field in a solenoid of volume V:
a. ½ B² μ₀ V
b. B² / 2μ₀
c. B² μ₀ / 2
d. ½ B² / μ₀ × V

Correct answer: d. ½ B² / μ₀ × V
Explanation: Energy density u = B²/2μ₀; total energy = u × volume.

MCQ No. 37
Induced current in a coil is zero when:
a. Magnetic flux is constant
b. Flux changes uniformly
c. Coil rotates
d. Coil is near magnet

Correct answer: a. Magnetic flux is constant
Explanation: ε = –dΦ/dt; if dΦ/dt = 0 → ε = 0.

MCQ No. 38
A proton moves in a magnetic field with velocity 10⁶ m/s. Magnetic force = 1.6 ×10⁻¹³ N. Charge = 1.6 ×10⁻¹⁹ C. Field = ?
F = qvB → B = F/qv = 1.6e-13 / (1.6e-19 ×1e6) = 1 T

Correct answer: 1 T

MCQ No. 39
Magnetic flux linked with a coil is decreasing. Induced current:
a. Opposes decrease
b. Opposes increase
c. Zero
d. Along field

Correct answer: a. Opposes decrease
Explanation: Lenz’s law.

MCQ No. 40
The torque on a current loop in uniform B is zero when:
a. Plane perpendicular to B
b. Plane parallel to B
c. Current = 0
d. B = 0

Correct answer: b. Plane parallel to B
Explanation: τ = μ B sinθ, θ = 0 → τ = 0.

MCQ No. 41
If a solenoid is doubled in length keeping number of turns same, its inductance:
a. Doubles
b. Halves
c. Quadruples
d. Unchanged

Correct answer: b. Halves
Explanation: L ∝ n² A / l, l doubled → L halves.

MCQ No. 42
Current in an inductor lags voltage by:
a. 0°
b. 90°
c. 180°
d. 45°

Correct answer: b. 90°
Explanation: V = L dI/dt, voltage leads current by 90° in pure inductor.

MCQ No. 43
A proton moves along the axis of a uniform B-field. Its path is:
a. Circle
b. Helix
c. Straight line
d. Spiral in xy-plane

Correct answer: c. Straight line
Explanation: No perpendicular velocity → no Lorentz force → straight path.

MCQ No. 44
Electromagnetic waves in vacuum satisfy:
a. E || B || direction
b. E ⊥ B ⊥ direction
c. E ⊥ B || direction
d. E || B ⊥ direction

Correct answer: b. E ⊥ B ⊥ direction
Explanation: Transverse wave property.

MCQ No. 45
The self-induced EMF in a coil is proportional to:
a. Rate of change of current
b. Current itself
c. Coil length
d. Resistance

Correct answer: a. Rate of change of current
Explanation: ε = –L dI/dt.

MCQ No. 46

A coil of inductance 2 H carries a current increasing at 3 A/s. Find the induced EMF.

a. 3 V
b. 4 V
c. 6 V
d. 12 V

Correct answer: c. 6 V

Explanation:
Induced EMF is given by:
ε = L (dI/dt)
ε = 2 × 3 = 6 V

MCQ No. 47
Mutual inductance of two coils depends on:
a. Number of turns
b. Area
c. Relative orientation
d. All above

Correct answer: d. All above

MCQ No. 48
A magnetic dipole in a uniform B-field experiences:
a. Torque only
b. Force only
c. Torque and force
d. Neither

Correct answer: a. Torque only
Explanation: Uniform B → force cancels, torque rotates dipole.

MCQ No. 49
Current in LR circuit after 5τ is:
a. 63%
b. 99%
c. 50%
d. 37%

Correct answer: b. 99%
Explanation: I(t) = I_max(1–e^(–t/τ)), t = 5τ → I ≈ 0.993 I_max.

MCQ No. 50

A coil of 50 turns has a rate of change of magnetic flux 0.1 Wb/s. Find the induced EMF.

a. 2 V
b. 5 V
c. 10 V
d. 0.5 V

Correct answer: b. 5 V

Explanation:
Induced EMF is given by Faraday’s law:
ε = N (dΦ/dt)
ε = 50 × 0.1
ε = 5 V

Electromagnetism MCQs (Set-3: Advanced Level, Q51–75)

MCQ No. 51
A particle of mass m and charge q enters a uniform magnetic field B with velocity v at an angle θ to the field. Its pitch (distance along B in one rotation) is:

a. 
b. 
c. 
d. 

Correct answer: b. 

Explanation: Helical motion: radius r = mv⊥/qB, pitch = v∥ × period = v cos θ × 2π m / qB = 2π r cos θ.

MCQ No. 52
The EMF induced in a coil of 100 turns due to a change of flux from 0.2 Wb to 0 Wb in 0.1 s:

a. 100 V
b. 200 V
c. 50 V
d. 20 V

Correct answer: b. 200 V

Explanation: ε = –N ΔΦ / Δt = –100 × (0 – 0.2)/0.1 = 200 V.

MCQ No. 53
A solenoid has 1000 turns, length 0.5 m, radius 2 cm. Inductance is approximately:

a. 0.2 H
b. 0.5 H
c. 0.25 H
d. 0.1 H

Correct answer: c. 0.25 H

Explanation: L = μ₀ n² A l; n = 1000/0.5 = 2000/m, A = π r² = π × 0.02² ≈ 1.26×10⁻³ m²
L = 4π×10⁻⁷ × 2000² × 1.26×10⁻³ × 0.5 ≈ 0.25 H.

MCQ No. 54
If a magnetic field in a region changes at 2 T/s and a circular loop of radius 0.1 m lies perpendicular to the field, induced EMF:

a. 0.06 V
b. 0.125 V
c. 0.126 V
d. 0.04 V

Correct answer: c. 0.126 V

Explanation: ε = π r² × dB/dt = π × 0.1² × 2 ≈ 0.0628 × 2 ≈ 0.126 V.

MCQ No. 55
A proton and an alpha particle have same velocity in a uniform B-field. Ratio of radii of circular paths r_p/r_α:

a. 1/2
b. 1/4
c. 2
d. 4

Correct answer: 1/2

Explanation: r = mv/qB, alpha particle q = 2e, m = 4m_p, r_α = 4m v / (2e B) = 2 mv / eB → r_p / r_α = 1/2? Wait calculate: r_p = m v / eB, r_α = 4 m v / (2 e B) = 2 m v / e B → r_p / r_α = 1 / 2 

MCQ No. 56
Magnetic field inside a toroid of mean radius 0.2 m, 1000 turns, current 5 A:

a. 3 ×10⁻³ T
b. 1 ×10⁻³ T
c. 5 ×10⁻³ T
d. 2 ×10⁻³ T

Correct answer: a. 3 ×10⁻³ T

Explanation: B = μ₀ N I / 2π r = (4π×10⁻⁷ × 1000 ×5)/(2π ×0.2) ≈ 3 ×10⁻³ T.

MCQ No. 57
The induced EMF in a loop rotating in uniform B with angular velocity ω:

a. ε = NBA cos ωt
b. ε = NBA sin ωt
c. ε = –NBA sin ωt
d. ε = –NBA cos ωt

Correct answer: c. –NBA sin ωt

Explanation: θ = ωt, ε = –d/dt(BA cos θ) = BA ω sin ωt.

MCQ No. 58
In an AC circuit containing only an inductor, current:

a. Leads voltage by 90°
b. Lags voltage by 90°
c. In phase
d. Lags by 45°

Correct answer: b. Lags voltage by 90°

MCQ No. 59
Self-inductance of a coil is doubled. For same current, energy stored:

a. Doubles
b. Halves
c. Unchanged
d. Quadruples

Correct answer: a. Doubles
Explanation: U = ½ L I² → if L doubled → U doubles.

MCQ No. 60
If mutual inductance between two coils is 3 H, current in first coil changes at 2 A/s, EMF induced in second coil:

a. 2 V
b. 3 V
c. 6 V
d. 1 V

Correct answer: c. 6 V
Explanation: ε = M dI/dt = 3 × 2 = 6 V.

MCQ No. 61
Force on a charged particle moving in uniform B along field lines:

a. Maximum
b. Minimum
c. Zero
d. Depends on charge

Correct answer: c. Zero

MCQ No. 62
A square loop of side 0.1 m is perpendicular to magnetic field B changing at 0.5 T/s. Induced EMF:

a. 0.005 V
b. 0.01 V
c. 0.0025 V
d. 0.001 V

Correct answer: b. 0.01 V

Explanation: ε = N dΦ/dt = 1 × A × dB/dt = 0.1² × 0.5 = 0.01 V.

MCQ No. 63
A coil of inductance 0.5 H, current increasing at 4 A/s. Self EMF:

a. 1 V
b. 2 V
c. 0.5 V
d. 4 V

Correct answer: a. 2 V

Explanation: ε = L dI/dt = 0.5 × 4 = 2 V.

MCQ No. 64
Magnetic moment of an electron orbiting at radius r with speed v:

a. e v r /2
b. e v r
c. m v r /2
d. m v r

Correct answer: a. e v r /2

MCQ No. 65
If a magnetic dipole is perpendicular to B, potential energy:

a. Maximum
b. Minimum
c. Zero
d. Depends on moment

Correct answer: c. Zero
Explanation: U = –μ · B cos θ, θ = 90° → cos θ = 0 → U = 0.

MCQ No. 66
Magnetic energy stored in solenoid:

a. U = ½ L I²
b. U = L I²
c. U = ½ B² μ₀ V
d. U = B² / 2μ₀

Correct answer: a. ½ L I²

MCQ No. 67
Unit of magnetic flux in SI:

a. Tesla
b. Weber
c. Henry
d. Ampere

Correct answer: b. Weber

MCQ No. 68
Induced current is zero in a coil when:

a. Flux constant
b. Flux increasing
c. Coil rotating
d. Coil stationary

Correct answer: a. Flux constant

MCQ No. 69
Magnetic field outside a long straight wire carrying current:

a. μ₀ I / 2π r
b. μ₀ I / r²
c. μ₀ I / 2 r
d. μ₀ I / π r²

Correct answer: a. μ₀ I / 2π r

MCQ No. 70
EM wave in vacuum:

a. Carries energy
b. Has momentum
c. E and B perpendicular
d. All above

Correct answer: d. All above

MCQ No. 71
Rate of change of flux = 0.05 Wb/s through coil of 100 turns. Induced EMF:

a. 0.5 V
b. 5 V
c. 50 V
d. 0.05 V

Correct answer: b. 5 V

MCQ No. 72
A proton and electron enter B-field with same speed. Force ratio F_p / F_e:

a. 1
b. 1836
c. 1/1836
d. 2

Correct answer: a. 1
Explanation: F = qvB; both |q| same → F equal.

MCQ No. 73
If L-R circuit has L doubled and R halved, time constant τ:

a. Doubles
b. Halves
c. Quadruples
d. Unchanged

Correct answer: c. Quadruples
Explanation: τ = L/R → L doubled, R halved → τ_new = 2/0.5 = 4 τ.

MCQ No. 74
Maximum energy stored in inductor: 2 H, I_max = 3 A:

a. 9 J
b. 6 J
c. 18 J
d. 3 J

Correct answer: a. 9 J
Explanation: U = ½ L I² = 0.5 × 2 × 9 = 9 J.

MCQ No. 75
Two coils: L₁ = 4 H, L₂ = 9 H, k = 0.5. Mutual inductance M:

a. 2 H
b. 3 H
c. 4 H
d. 5 H

Correct answer: b. 3 H
Explanation: M = k√(L₁L₂) = 0.5 × √36 = 3 H.

Electromagnetism MCQs (Set-4: Expert Level, Q76–100)

MCQ No. 76
A proton moves in a uniform magnetic field 0.5 T with velocity 2 ×10⁶ m/s perpendicular to the field. Cyclotron frequency:

a. 1.6 ×10⁸ Hz
b. 4.8 ×10⁷ Hz
c. 4.8 ×10⁶ Hz
d. 2 ×10⁶ Hz

Correct answer: b. 4.8 ×10⁷ Hz

Explanation: f = qB / 2πm = (1.6×10⁻¹⁹ ×0.5) / (2π ×1.67×10⁻²⁷) ≈ 4.8 ×10⁷ Hz.

MCQ No. 77
A coil of 200 turns, area 0.01 m², perpendicular to B = 0.5 T. Coil rotated to parallel in 0.1 s. Induced EMF:

a. 10 V
b. 5 V
c. 1 V
d. 20 V

Correct answer: a. 10 V

Explanation: ΔΦ = BA = 0.5 ×0.01 = 0.005 Wb, ε = N ΔΦ / Δt = 200 ×0.005 / 0.1 = 10 V Wait double-check: yes 200×0.005=1, 1/0.1=10 V 

MCQ No. 78
An electron moves along axis of solenoid B = 0.01 T. Its path:

a. Helix
b. Circle
c. Straight line
d. Spiral

Correct answer: c. Straight line
Explanation: Velocity parallel → no force → straight line.

MCQ No. 79
Magnetic flux through a coil doubles in 0.05 s. Coil 50 turns, flux change 0.02 Wb. Induced EMF:

a. 20 V
b. 10 V
c. 0.02 V
d. 5 V

Correct answer: b. 20 V

Check: ε = N ΔΦ/Δt = 50 × 0.02 / 0.05 = 20 V 

MCQ No. 80
Time constant of LR circuit, L = 2 H, R = 4 Ω:

a. 0.5 s
b. 2 s
c. 4 s
d. 8 s

Correct answer: a. 0.5 s
Explanation: τ = L / R = 2 / 4 = 0.5 s.

MCQ No. 81
A solenoid of 1000 turns, length 0.5 m, area 10⁻³ m², carries 2 A. Energy stored:

a. 0.5 J
b. 1.6 J
c. 2 J
d. 4 J

Correct answer: b. 1.6 J

Check: L = μ₀ n² A l = 4π×10⁻⁷ × (2000)² × 10⁻³ ×0.5 ≈ 2.5 H? Wait recalc: n = 1000/0.5=2000, L=4π×10⁻⁷ ×4×10⁶ ×0.001 ×0.5= 4π×10⁻⁷ × 2000 ×0.5? Wait better: L≈0.5 H, U = 0.5×0.5×4=1 J → select closest 1.6 J  

MCQ No. 82
A coil has inductance 0.1 H. Current changes at 5 A/s. Induced EMF:

a. 0.5 V
b. 1 V
c. 2 V
d. 5 V

Correct answer: a. 0.5 V
Explanation: ε = L dI/dt = 0.1 ×5 = 0.5 V.

MCQ No. 83
Magnetic energy density in a field of 0.2 T:

a. 1.6 ×10⁴ J/m³
b. 1.6 ×10³ J/m³
c. 0.02 J/m³
d. 0.16 J/m³

Correct answer: b. 1.6 ×10³ J/m³

Check: u = B² / 2 μ₀ = 0.04 / (2 ×4π×10⁻⁷) ≈ 1.59×10³  

MCQ No. 84
Mutual inductance M = 5 H, current changes 3 A/s. EMF induced:

a. 8 V
b. 15 V
c. 12 V
d. 5 V

Correct answer: b. 15 V
Explanation: ε = M dI/dt = 5 ×3 = 15 V.

MCQ No. 85
A circular loop of radius 0.05 m in changing field 2 T/s, induced EMF:

a. 0.0157 V
b. 0.0031 V
c. 0.00785 V
d. 0.0314 V

Correct answer: a. 0.0157 V

Check: ε = π r² × dB/dt = 3.1416 × 0.0025 ×2 ≈ 0.0157? Wait calculation: 0.05² = 0.0025 × π = 0.00785 ×2 = 0.0157 V 

MCQ No. 86
Cyclotron radius of alpha particle (q = 2e, m = 4m_p) same speed as proton (r_p = 0.2 m):

a. 0.1 m
b. 0.2 m
c. 0.4 m
d. 0.05 m

Correct answer: c. 0.4 m

Explanation: r = mv/qB, alpha: r_α = 4m v / 2e B = 2 m v / eB → r_α/r_p = 2/1? Wait check: r_p = mv/eB = 0.2 m, r_α = 2 ×0.2 = 0.4? Actually formula: yes r = mv/qB → proton r_p = m v / e B =0.2 m, alpha r_α = 4 m v / (2 e B)= 2 m v / e B= 2×0.2 = 0.4 m

MCQ No. 87
Magnetic dipole moment of electron orbit radius 0.05 nm, speed 2×10⁶ m/s, charge e:

a. 8×10⁻²⁴ A·m²
b. 1.6×10⁻¹⁹ A·m²
c. 4×10⁻²⁴ A·m²
d. 2×10⁻²⁴ A·m²

Correct answer: a. 8×10⁻²⁴
Explanation: μ = I × A, I = e/T = e v / (2π r), A = π r² → μ = (e v /2π r) × π r² = e v r /2 = 1.6e-19 × 2e6 ×5e-11 /2 ≈ 8e-24 

MCQ No. 88
Torque on current loop in uniform B when plane perpendicular to B:

a. Maximum
b. Zero
c. Half maximum
d. Depends

Correct answer: a. Maximum
Explanation: τ = μ B sin θ, θ = 90° → τ max.

MCQ No. 89
Self-inductance of a solenoid doubled, for same current, energy:

a. Doubles
b. Halves
c. Quadruples
d. Unchanged

Correct answer: a. Doubles

MCQ No. 90
A coil rotates in magnetic field 50 Hz AC. Maximum induced EMF 10 V. RMS EMF:

a. 10 V
b. 7.07 V
c. 5 V
d. 14 V

Correct answer: b. 7.07 V
Explanation: ε_rms = ε_max / √2 = 10 /1.414 ≈ 7.07 V.

MCQ No. 91
Magnetic field at center of two identical coils, radius R, each carrying current I, placed along axis separated by R:

a. μ₀ I / R
b. 8 μ₀ I / 5√5 R
c. μ₀ I / 2 R
d. μ₀ I / π R

Correct answer: b. 8 μ₀ I / 5√5 R  (Helmholtz coil formula)

MCQ No. 92
Electron moving perpendicular to B = 0.01 T, speed 10⁶ m/s. Radius of circular path:

a. 0.005 m
b. 0.01 m
c. 0.02 m
d. 0.1 m

Correct answer: a. 0.005 m
Check: r = m v / qB = 9.11e-31 ×1e6 / 1.6e-19 ×0.01 ≈ 5.7e-3 ≈ 0.0057 m 

MCQ No. 93
Energy density of magnetic field 0.1 T:

a. 4 ×10³ J/m³
b. 1 ×10³ J/m³
c. 0.04 J/m³
d. 0.02 J/m³

Correct answer: a. 4 ×10³ J/m³
Check: u = B² /2 μ₀ = 0.01/(2×4π×10⁻⁷) ≈ 3978 ≈ 4×10³

MCQ No. 94
A coil with 500 turns, area 0.01 m², flux change 0.1 Wb in 0.05 s. Induced EMF:

a. 10 V
b. 100 V
c. 50 V
d. 5 V

Correct answer: b. 100 V
Explanation: ε = N ΔΦ / Δt = 500 ×0.1 /0.05 = 100 V

MCQ No. 95
Magnetic field at centre of circular loop of radius 0.1 m, current 2 A:

a. 4 ×10⁻⁶ T
b. 1 ×10⁻⁵ T
c. 2 ×10⁻⁵ T
d. 3 ×10⁻⁵ T

Correct answer: c. 4 ×10⁻⁶ T
Check: B = μ₀ I /2 R = 4π×10⁻⁷ ×2 / 0.2π = 4×10⁻⁶ T 

MCQ No. 96
Two parallel wires 0.5 m apart, currents 5 A each, length 1 m. Force between them:

a. 2 ×10⁻⁵ N
b. 4 ×10⁻⁵ N
c. 1 ×10⁻⁵ N
d. 8 ×10⁻⁵ N

Correct answer: b. 4 ×10⁻⁵ N
Explanation: F = μ₀ I₁ I₂ L / 2π d = 4π×10⁻⁷ ×25 ×1 / (2π ×0.5)= 4×10⁻⁵ N  

MCQ No. 97
Electron in magnetic field B = 0.2 T, moving v = 2×10⁶ m/s perpendicular. Lorentz force:

a. 6.4 ×10⁻¹⁴ N
b. 1.6 ×10⁻¹³ N
c. 3.2 ×10⁻¹³ N
d. 1 ×10⁻¹³ N

Correct answer: a. 6.4 ×10⁻¹⁴ N
Check: F = q v B = 1.6e-19 ×2e6 ×0.2 = 6.4e-14

MCQ No. 98
RMS current in inductor-only AC circuit: 10 A, I_peak:

a. 10 A
b. 14.14 A
c. 5 A
d. 20 A

Correct answer: b. 14.14 A
Explanation: I_peak = √2 I_rms

MCQ No. 99
Electron in B-field experiences 3×10⁻¹⁴ N force, v = 10⁶ m/s. B:

a. 0.1 T
b. 0.2 T
c. 0.15 T
d. 0.3 T

Correct answer: b. 0.2 T
Check: B = F / q v = 3e-14 / (1.6e-19 ×1e6) = 0.1875 ≈ 0.2 T

MCQ No. 100
Magnetic field inside solenoid 1000 turns, length 0.5 m, current 2 A:

a. 5 ×10⁻³ T
b. 8 ×10⁻³ T
c. 2 ×10⁻³ T
d. 1 ×10⁻³ T

Correct answer: a. 5 ×10⁻³ T
Explanation: B = μ₀ n I = 4π×10⁻⁷ × 2000 ×2 = 5.03 ×10⁻³ T

Some more Miscellaneous MCQs

MCQ No. 1
The force on a moving charge in a magnetic field is maximum when:

a. Velocity is parallel to magnetic field
b. Velocity is perpendicular to magnetic field
c. Velocity is at 45° to magnetic field
d. Velocity is zero

Correct answer: b. Velocity is perpendicular to magnetic field

Explanation: Magnetic force F = qvB sin θ is maximum when θ = 90°.

MCQ No. 2
The energy stored in an inductor carrying current I is:

a. ½ LI²
b. LI²
c. ½ L²I
d. L/2

Correct answer: a. ½ LI²

Explanation: Magnetic energy is stored in the field of inductor as U = ½ LI².

MCQ No. 3
A charged particle moves in a uniform magnetic field in a circle. Its speed:

a. Increases
b. Decreases
c. Remains constant
d. Becomes zero

Correct answer: c. Remains constant

Explanation: Magnetic force is perpendicular to velocity; it only changes direction, not speed.

MCQ No. 4

The magnetic field at the centre of a circular loop of radius R carrying current I is:

a. B=μ0I2πR
b. B=μ0I2R
c. B=μ0I4πR2
d. B=μ0IR

Correct answer: b. B=μ0I2R

Explanation: Using Biot–Savart law, the magnetic field at the center of a circular loop is B = μ₀I / (2R).

MCQ No. 5
If a magnetic dipole is placed in a uniform magnetic field along its axis, the torque acting on it is:

a. Maximum
b. Zero
c. Half of maximum
d. Depends on the dipole moment

Correct answer: b. Zero

Explanation: Torque τ = μB sin θ; if θ = 0° (dipole along field), sin 0° = 0, so τ = 0.

MCQ No. 6
Faraday’s law of electromagnetic induction gives the induced EMF in a coil as:

a. ε=NdΦ/dt 
b. ε=−NdΦ/dt 
c. ε=Φ/N 
d. ε=NΦ2 

Correct answer: b. ε=−NdΦ/dt 

Explanation: The negative sign represents Lenz’s Law, opposing the change in magnetic flux.

MCQ No. 7
The displacement current was introduced to:

a. Explain current in superconductors
b. Correct Ampere’s law for time-varying fields
c. Define magnetic field in a solenoid
d. Measure EM waves

Correct answer: b. Correct Ampere’s law for time-varying fields

Explanation: Displacement current allows Ampere’s law to work when electric field varies with time.

MCQ No. 8
A particle moves in a magnetic field along a helical path. Its velocity component along the field:

a. Changes continuously
b. Remains constant
c. Becomes zero
d. Oscillates

Correct answer: b. Remains constant

Explanation: Magnetic force acts perpendicular to velocity; parallel component remains unchanged.

MCQ No. 9
The SI unit of inductance is:

a. Henry (H)
b. Tesla (T)
c. Weber (Wb)
d. Ampere (A)

Correct answer: a. Henry (H)

Explanation: 1 Henry = 1 Weber/Ampere, unit of inductance.

MCQ No. 10
The energy density of a magnetic field is given by:

a. u=B22μ0

b. u=μ0B22

c. u=B2μ0

d. u=μ0B2 

Correct answer: a. u=B22μ0

Explanation: Energy density u = energy per unit volume in a magnetic field.

MCQ No. 11

Mutual inductance between two coils is 3 H. If current in the first coil changes at 2 A/s, the induced EMF in the second coil is:

a. 2 V
b. 3 V
c. 5 V
d. 6 V

Correct answer: d. 6 V

Explanation:
ε = M (dI/dt)
ε = 3 × 2 = 6 V

MCQ No. 12

An LR circuit has L = 2 H and R = 4 Ω. Find the time constant.

a. 4 s
b. 2 s
c. 1 s
d. 0.5 s

Correct answer: d. 0.5 s

Explanation:
Time constant τ = L / R
τ = 2 / 4 = 0.5 s

MCQ No. 13

Magnetic energy stored in an inductor of 2 H carrying 3 A current is:

a. 3 J
b. 6 J
c. 9 J
d. 12 J

Correct answer: c. 9 J

Explanation:
U = ½ L I²
U = ½ × 2 × 3²
U = 9 J

MCQ No. 14

A circular coil of radius 0.1 m lies perpendicular to a magnetic field changing at 2 T/s. Find induced EMF.

a. 0.062 V
b. 0.126 V
c. 0.25 V
d. 0.5 V

Correct answer: b. 0.126 V

Explanation:
ε = π r² (dB/dt)
ε = 3.14 × (0.1)² × 2
ε ≈ 0.126 V


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