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]

0%

(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]

0%

(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]

0%

(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)

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

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]

0%

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%

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]

0%

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]

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