Electromagnetic Induction | Physics JEE Main questions with Solutions

Q 1 :

A rectangular loop of length 2.5 m and width 2 m is placed at 60° to a magnetic field of 4T. The loop is removed from the field in 10 sec. The average emf induced in the loop during this time is [2024]

$- 2 V$
$+ 2 V$
$+ 1 V$
$- 1 V$

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(3)

$e = - \frac{0 - (4 \times (2.5 \times 2) \cos 60 °)}{10} = + 1 V$

Q 2 :

A coil is placed perpendicular to a magnetic field of 5000T. When the field is changed to 3000T in 2s, an induced emf of 22 V is produced in the coil. If the diameter of the coil is 0.02 m, then the number of turns in the coil is [2024]

70
140
35
7

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(1)

$ε = N (\frac{Δ ϕ}{t})$

$Δ ϕ = (Δ B) A$

$B_{i} = 5000 T, B_{f} = 3000 T$

$Δ ϕ = (Δ B) A = (2000) π {(0.01)}^{2} = 0.2 π$

$ε = N (\frac{Δ ϕ}{t}) \Rightarrow 22 = N (\frac{0.2 π}{2})$

$\Rightarrow N = 70$

Q 3 :

The magnetic flux $ϕ$ (in weber) linked with a closed circuit of resistance 8 Ω varies with time (in seconds) as $ϕ = 5 t^{2} - 36 t + 1$ . The induced current in the circuit at t = 2s is _____ A. [2024]

(2) $ε = - (\frac{d ϕ}{d t}) = - 10 t + 36$

$at t = 2 s, ε = 16 V$

$i = \frac{ε}{R} = \frac{16}{8} = 2 A$

Q 4 :

A square loop of side 15 cm being moved towards right at a constant speed of 2 cm/s as shown in the figure. The front edge enters the 50 cm wide magnetic field at t = 0. The value of induced emf in the loop at t = 10 s will be [2024]

0.3 mV
4.5 mV
zero
3 mV

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(3)

At $t = 10$ sec. distance moved by loop;

$d = v \times t = 2 \times 10 = 20 cm$

i.e. loop is completely inside the field. At $t = 10$ sec there is no change in flux

Now, emf induced, $E = \frac{d ϕ}{d t} = B \frac{d A}{d t} = 0$

Q 5 :

A square loop of side 10 cm and resistance 0.7 $Ω$ is placed vertically in east-west plane. A uniform magnetic field of 0.20T is set up across the plane in northeast direction. The magnetic field is decreased to zero in 1s at a steady rate. Then, magnitude of induced emf is $\sqrt{x} \times 10^{- 3}$ V. The value of $x$ is ______. [2024]

(2)

$\vec{A} = {(0.1)}^{2} \hat{j}$

$\vec{B} = \frac{0.2}{\sqrt{2}} \hat{i} + \frac{0.2}{\sqrt{2}} \hat{j}$

Magnitude of induced emf

$e = \frac{Δ ϕ}{Δ t} = \frac{\vec{B} \cdot \vec{A} - 0}{1} = \sqrt{2} \times 10^{- 3} V$

Q 6 :

A coil of 200 turns and area 0.20 $m^{2}$ is rotated at half a revolution per second and is placed in a uniform magnetic field of 0.01T perpendicular to the axis of rotation of the coil. The maximum voltage generated in the coil is $\frac{2 π}{β}$ volt. The value of $β$ is ______. [2024]

(5)

$ϕ = N B A \cos θ$

$ε = - \frac{d ϕ}{d t} = - \frac{d}{d t} (N B A \cos θ)$

$ε = N B A \sin θ \cdot \frac{d θ}{d t} = (N B A ω) \sin θ$

$ε_{\max} at θ = 90 °, ε_{\max} = N B A ω$

$ε_{\max} = 200 \times 0.01 \times 0.2 \times π = 200 \times \frac{1}{100} \times \frac{2}{10} \times π$

$ε_{\max} = \frac{4 π}{10} = \frac{2 π}{5}, ε_{\max} = \frac{2 π}{β} so β = 5$

Q 7 :

A coil of area A and N turns is rotating with angular velocity $ω$ in a uniform magnetic field $\vec{B}$ about an axis perpendicular to $\vec{B}$ . Magnetic flux $φ$ and induced emf $ε$ across it, at an instant when $\vec{B}$ is parallel to the plane of coil, are: [2025]

$φ = A B, ε = 0$
$φ = 0, ε = N A B ω$
$φ = 0, ε = 0$
$φ = A B, ε = N A B ω$

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(2)

$ϕ = N B A \cos θ$

$ε = - \frac{d ϕ}{d t} = - N B A \frac{d (\cos θ)}{d t}$

$θ = ω t$

$ε = - N B A ω \sin ω t$

if B is parallel to plane of coil

$ω = 90 °$

$ϕ = 0, E = B A ω N$

Q 8 :

A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnate field, the plot of magnitude of induced emf ( $ε$ ) with time (t) is given by [2025]

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(4)

Motional emf : $ε = B l v$ = constant

Q 9 :

A conducting circular loop of radius $\frac{10}{\sqrt{π}}$ cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is [2023]

emf = 1 mV
emf = 100 mV
emf = 5 mV
emf = 10 mV

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(4)

$EMF = \frac{d ϕ}{d t} = \frac{B A - 0}{t}$

$A = π r^{2} = π (\frac{0 . 1^{2}}{π}) = 0.01$

$B = 0.5$

$EMF = \frac{(0.5) (0.01)}{0.5} = 0.01 V = 10 mV$

Q 10 :

A coil is placed in a magnetic field such that the plane of the coil is perpendicular to the direction of the magnetic field. The magnetic flux through a coil can be changed. [2023]

A. by changing the magnitude of the magnetic field within the coil.
B. by changing the area of the coil within the magnetic field.
C. by changing the angle between the direction of the magnetic field and the plane of the coil.
D. by reversing the magnetic field direction abruptly without changing its magnitude.

Choose the most appropriate answer from the options given below:

A and B only
A, B and C only
A, B and D only
A and C only

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(2)

$ϕ = \vec{B} \cdot \vec{A} = B A \cos θ$

Q 11 :

A rod with circular cross-section area $2 {cm}^{2}$ and length 40 cm is wound uniformly with 400 turns of an insulated wire. If a current of 0.4 A flows in the wire windings, the total magnetic flux produced inside the windings is $4 π \times 10^{- 6} Wb$ . The relative permeability of the rod is (Given: Permeability of vacuum $μ_{0} = 4 π \times 10^{- 7} {NA}^{- 2}$ ). [2023]

$12.5$
$\frac{32}{5}$
$125$
$\frac{5}{16}$

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(3)

$ϕ = μ_{r} μ_{0} \frac{N}{l} I \times A \Rightarrow μ_{r} = 125$

Q 12 :

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B = 0.8 T. When released, the radius of the loop starts shrinking at a constant rate of $2 {cm s}^{- 1}$ . The induced emf in the loop at an instant when the radius of the loop is 10 cm will be ________ mV. [2023]

(10)

$EMF = \frac{d}{d t} (B π r^{2})$

$= 2 B π r \frac{d r}{d t} = 2 \times π \times 0.1 \times 0.8 \times 2 \times 10^{- 2}$

$= 2 π \times 1.6 = 10.06 [round off 10.06 = 10]$

Q 13 :

A square shaped coil of area $70 {cm}^{2}$ having 600 turns rotates in a magnetic field of $0.4 {Wbm}^{- 2}$ , about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes 500 revolution in a minute, the instantaneous emf when the plane of the coil is inclined at $60 °$ with the field, will be ________ V. [2023]

(Take $π = \frac{22}{7}$ )

(44)

$N = 600, A = 70 \times 10^{- 4} m^{2}, B = 0.4 T$

$ω = \frac{500 \times 2 π}{60} = \frac{100 π}{6} rad/s$

$E = N A B ω \sin ω t$

$ω t is the angle between \vec{A} and \vec{B}$

$= 600 \times 70 \times 10^{- 4} \times 0.4 \times \frac{100 π}{6} \times \frac{1}{2} = 44 V$

Q 14 :

A square loop of side 2.0 cm is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude 2.5 A and angular frequency $700 {rad s}^{- 1}$ . The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is $x \times 10^{- 4} V$ . The value of $x$ is _______ (Take $π = \frac{22}{7}$ ) [2023]

(44)

$B_{due to solenoid} = μ_{0} n I$

$ϕ_{through square} = μ_{0} n I \times A (A = Area)$

$EMF = μ_{0} n A \times \frac{d I}{d t} = μ_{0} n A \times I_{0} ω \cos ω t$

$EMF amplitude = μ_{0} n A \times I_{0} ω$

$= 4 π \times 10^{- 7} \times \frac{50}{10^{- 2}} \times 4 \times 10^{- 4} \times 2.5 \times 700$

$= 44 \times 10^{- 4} V$

Q 15 :

The magnetic field B crossing normally a square metallic plate of area ${4m}^{2}$ is changing with time as shown in the figure. The magnitude of induced emf in the plate during $t = 2 s$ to $t = 4 s$ is __________ mV. [2023]

(8)

$m = \tan θ = \frac{10}{5} = 2$

$B = m t$

$B = 2 t$

$ε =$ $| \frac{d ϕ}{d t} |$ $= \frac{d (B A)}{d t} = \frac{A d B}{d t}$

$ε = \frac{4 d (2 t)}{d t} = 4 \times 2 = 8 mV$

Q 16 :

A conducting circular loop is placed in a uniform magnetic field of 0.4 T with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of 1 mm/s. The magnitude of induced emf in the loop at an instant when the radius of the loop is 2 cm will be _________ $μ V$ . [2023]

(50)

$\frac{d r}{d t} = 10^{- 3} m/s$

$\frac{d A}{d t} = 2 π r \frac{d r}{d t}$

$ε =$ $| \frac{- d ϕ}{d t} |$ $=$ $| \frac{B d A}{d t} |$

$= 0.4 \times 2 \times π \times 2 \times 10^{- 2} \times 10^{- 3} V$

$= 16 π μ V = 50.24 μ V$

Q 17 :

An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of cross-sectional area $24 {cm}^{2}$ . The two ends of the wire are connected to a resistor. The total resistance in the circuit is $12 Ω$ . If an externally applied uniform magnetic field in the core along its axis changes from 1.5 T in one direction to 1.5 T in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be _____ mC. [2023]

(60)

$Δ Q = - \frac{Δ ϕ}{R} = - (\frac{ϕ_{2} - ϕ_{1}}{R})$

$ϕ_{1} = N B A$

$ϕ_{2} = - N B A$

$∴$ $Δ Q = \frac{2 N B A}{R} = \frac{2 \times 100 \times 1.5 \times 24 \times 10^{- 4}}{12}$

$= 6 \times 10^{- 2} C = 60 mC$

Q 18 :

A conducting circular loop of area $1.0 m^{2}$ is placed perpendicular to a magnetic field which varies as $B = \sin (100 t) Tesla .$ If the resistance of the loop is $100 Ω$ , then the average thermal energy dissipated in the loop in one period is ______ J. [2026]

$\frac{π}{2}$
$π$
$π^{2}$
$2 π$

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(2)

Area of the loop = $1 m^{2}$

$B = \sin (100 t)$

$∴$ $ϕ = B A = \sin (100 t)$

$∴$ $\frac{d ϕ}{d t} = 100 \cos (100 t)$

$∴$ $P = \frac{V^{2}}{R} = \frac{10^{4} \cos^{2} (100 t)}{100}$

$∴$ $Thermal energy dissipated in 1 time period$

$= \int_{0}^{T} P d t = \int_{0}^{T} 100 \cos^{2} (100 t) d t$

$T = \frac{2 π}{100} = \frac{π}{50} sec$

$∴$ $Q = 100 \int_{0}^{π / 50} \cos^{2} (100 t) d t$

$= 100 \int_{0}^{π / 50} \frac{1 + \cos (200 t)}{2} d t$

$= 100 [\frac{π}{100}] = π$

Q 19 :

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop is ____ mV. [2026]

13.2
1.32
8.25
6.6

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(2)

$induced EMF = \frac{d ϕ}{d t}$

$circumference ≃ 14 π$

$side length of square loop = \frac{14 π}{4} = \frac{7 π}{2}$

$Δ ϕ = B (A_{1} - A_{2})$

$= (0.2) [(\frac{7 π}{2}) \times \frac{7 π}{2} - 49 π] \times 10^{- 4}$

$= 0.2 (\frac{49 π^{2}}{4} - 49 π) \times 10^{- 4}$

$Δ ϕ = 0.2 \times 33.07 \times 10^{- 4}$

$Δ ϕ = 6.614 \times 10^{- 4}$

$EMF = \frac{6.614 \times 10^{- 4}}{\frac{1}{2}} V = 13.23 \times 10^{- 4} V$

$EMF = 1.32 mV$

Q 20 :

A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad/s in a magnetic field of 0.5 T perpendicular to the axis of rotation. When the loop is rotated by $30 °$ from the horizontal position, the induced EMF is 15.4 mV. The radius of the loop is ________ mm.

$(Take π = \frac{22}{7})$ [2026]

(14)

$E = B ω A \sin ω t$

$15.4 \times 10^{- 3} = \frac{1}{2} \times 100 \times \frac{22}{7} r^{2} \times \frac{1}{2}$

$r = \sqrt{\frac{15.4 \times 28 \times 10^{- 5}}{22}}$

$R = 14 mm$

Topic Question Set

Q 1 :

A rectangular loop of length 2.5 m and width 2 m is placed at 60° to a magnetic field of 4T. The loop is removed from the field in 10 sec. The average emf induced in the loop during this time is [2024]

Q 2 :

A coil is placed perpendicular to a magnetic field of 5000T. When the field is changed to 3000T in 2s, an induced emf of 22 V is produced in the coil. If the diameter of the coil is 0.02 m, then the number of turns in the coil is [2024]

Q 3 :

The magnetic flux $ϕ$ (in weber) linked with a closed circuit of resistance 8 Ω varies with time (in seconds) as $ϕ = 5 t^{2} - 36 t + 1$ . The induced current in the circuit at t = 2s is _____ A. [2024]

Q 4 :

A square loop of side 15 cm being moved towards right at a constant speed of 2 cm/s as shown in the figure. The front edge enters the 50 cm wide magnetic field at t = 0. The value of induced emf in the loop at t = 10 s will be [2024]

Q 6 :

A coil of 200 turns and area 0.20 $m^{2}$ is rotated at half a revolution per second and is placed in a uniform magnetic field of 0.01T perpendicular to the axis of rotation of the coil. The maximum voltage generated in the coil is $\frac{2 π}{β}$ volt. The value of $β$ is ______. [2024]

Q 7 :

A coil of area A and N turns is rotating with angular velocity $ω$ in a uniform magnetic field $\vec{B}$ about an axis perpendicular to $\vec{B}$ . Magnetic flux $φ$ and induced emf $ε$ across it, at an instant when $\vec{B}$ is parallel to the plane of coil, are: [2025]

Q 8 :

A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnate field, the plot of magnitude of induced emf ( $ε$ ) with time (t) is given by [2025]

Q 9 :

A conducting circular loop of radius $\frac{10}{\sqrt{π}}$ cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is [2023]

Q 15 :

The magnetic field B crossing normally a square metallic plate of area ${4m}^{2}$ is changing with time as shown in the figure. The magnitude of induced emf in the plate during $t = 2 s$ to $t = 4 s$ is __________ mV. [2023]

Q 18 :

A conducting circular loop of area $1.0 m^{2}$ is placed perpendicular to a magnetic field which varies as $B = \sin (100 t) Tesla .$ If the resistance of the loop is $100 Ω$ , then the average thermal energy dissipated in the loop in one period is ______ J. [2026]

Q 19 :

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop is ____ mV. [2026]

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Topic Question Set

Q 1 : A rectangular loop of length 2.5 m and width 2 m is placed at 60° to a magnetic field of 4T. The loop is removed from the field in 10 sec. The average emf induced in the loop during this time is [2024]

Q 2 : A coil is placed perpendicular to a magnetic field of 5000T. When the field is changed to 3000T in 2s, an induced emf of 22 V is produced in the coil. If the diameter of the coil is 0.02 m, then the number of turns in the coil is [2024]

Q 3 : The magnetic flux ϕ (in weber) linked with a closed circuit of resistance 8 Ω varies with time (in seconds) as ϕ=5t2-36t+1. The induced current in the circuit at t = 2s is _____ A. [2024]

Q 4 : A square loop of side 15 cm being moved towards right at a constant speed of 2 cm/s as shown in the figure. The front edge enters the 50 cm wide magnetic field at t = 0. The value of induced emf in the loop at t = 10 s will be [2024]

Q 6 : A coil of 200 turns and area 0.20 m2 is rotated at half a revolution per second and is placed in a uniform magnetic field of 0.01T perpendicular to the axis of rotation of the coil. The maximum voltage generated in the coil is 2πβ volt. The value of β is ______. [2024]

Q 7 : A coil of area A and N turns is rotating with angular velocity ω in a uniform magnetic field B→ about an axis perpendicular to B→. Magnetic flux φ and induced emf ε across it, at an instant when B→ is parallel to the plane of coil, are: [2025]

Q 8 : A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnate field, the plot of magnitude of induced emf (ε) with time (t) is given by [2025]

Q 9 : A conducting circular loop of radius 10π cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is [2023]

Q 15 : The magnetic field B crossing normally a square metallic plate of area 4m2 is changing with time as shown in the figure. The magnitude of induced emf in the plate during t=2 s to t=4 s is __________ mV. [2023]

Q 18 : A conducting circular loop of area1.0 m2 is placed perpendicular to a magnetic field which varies as B=sin(100t) Tesla. If the resistance of the loop is 100 Ω, then the average thermal energy dissipated in the loop in one period is ______ J. [2026]

Q 19 : A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop is ____ mV. [2026]

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Q 1 :

A rectangular loop of length 2.5 m and width 2 m is placed at 60° to a magnetic field of 4T. The loop is removed from the field in 10 sec. The average emf induced in the loop during this time is [2024]

Q 2 :

A coil is placed perpendicular to a magnetic field of 5000T. When the field is changed to 3000T in 2s, an induced emf of 22 V is produced in the coil. If the diameter of the coil is 0.02 m, then the number of turns in the coil is [2024]

Q 3 :

The magnetic flux $ϕ$ (in weber) linked with a closed circuit of resistance 8 Ω varies with time (in seconds) as $ϕ = 5 t^{2} - 36 t + 1$ . The induced current in the circuit at t = 2s is _____ A. [2024]

Q 4 :

A square loop of side 15 cm being moved towards right at a constant speed of 2 cm/s as shown in the figure. The front edge enters the 50 cm wide magnetic field at t = 0. The value of induced emf in the loop at t = 10 s will be [2024]

Q 6 :

A coil of 200 turns and area 0.20 $m^{2}$ is rotated at half a revolution per second and is placed in a uniform magnetic field of 0.01T perpendicular to the axis of rotation of the coil. The maximum voltage generated in the coil is $\frac{2 π}{β}$ volt. The value of $β$ is ______. [2024]

Q 7 :

A coil of area A and N turns is rotating with angular velocity $ω$ in a uniform magnetic field $\vec{B}$ about an axis perpendicular to $\vec{B}$ . Magnetic flux $φ$ and induced emf $ε$ across it, at an instant when $\vec{B}$ is parallel to the plane of coil, are: [2025]

Q 8 :

A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnate field, the plot of magnitude of induced emf ( $ε$ ) with time (t) is given by [2025]

Q 9 :

A conducting circular loop of radius $\frac{10}{\sqrt{π}}$ cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is [2023]

Q 15 :

The magnetic field B crossing normally a square metallic plate of area ${4m}^{2}$ is changing with time as shown in the figure. The magnitude of induced emf in the plate during $t = 2 s$ to $t = 4 s$ is __________ mV. [2023]

Q 18 :

A conducting circular loop of area $1.0 m^{2}$ is placed perpendicular to a magnetic field which varies as $B = \sin (100 t) Tesla .$ If the resistance of the loop is $100 Ω$ , then the average thermal energy dissipated in the loop in one period is ______ J. [2026]

Q 19 :

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop is ____ mV. [2026]