Electromagnetic Induction | Physics JEE Main questions with Solutions

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]

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(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 $π = \frac{22}{7}$ )

0%

(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]

0%

(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]

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(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]

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(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]

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(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)

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]

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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]

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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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