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]

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

1

2

3

4

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

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

1

2

3

4

(A) $ε = N (\frac{Δ ϕ}{t})$

$Δ ϕ = (Δ B) A$

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

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

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

$\Rightarrow N = 70$

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

1

2

3

4

(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)

$ϕ = N B A \cos θ$

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

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

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

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

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

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%

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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]

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 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]

0%

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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]