(C) Given: Magnetic field $B = 0.4 \ \text{T}$,Radius $R = 20 \ \text{cm} = 0.2 \ \text{m}$,Angular velocity $\omega = 10 \pi \ \text{rad s}^{-1}$.The

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(C) Given: Magnetic field $B = 0.4 \ \text{T}$,Radius $R = 20 \ \text{cm} = 0.2 \ \text{m}$,Angular velocity $\omega = 10 \pi \ \text{rad s}^{-1}$.The induced electromotive force $(EMF)$ or potential difference between the center and the rim of a rotating disc in a magnetic field is given by the formula:$E = \frac{1}{2} B \omega R^2$Substituting the given values:$E = \frac{1}{2} \times 0.4 \times (10 \pi) \times (0.2)^2$$E = 0.2 \times 10 \times 3.14 \times 0.04$$E = 2 \times 3.14 \times 0.04$$E = 6.28 \times 0.04 = 0.2512 \ \text{V}$Thus,the potential difference developed is $0.2512 \ \text{V}$.

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

Medium

$A$ uniform magnetic field of $0.4 \ \text{T}$ acts perpendicular to a circular copper disc $20 \ \text{cm}$ in radius. The disc is rotating with a uniform angular velocity of $10 \pi \ \text{rad s}^{-1}$ about an axis passing through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim (in $\text{V}$)? $(\pi = 3.14)$

JEE MAIN 2025 All JEE MAIN

A
$0.0628$
B
$0.5024$
C
$0.2512$
D
$0.1256$

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Electromagnetic Induction

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Motional EMI (Induced Parameter)

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As shown in the figure,a metal rod makes contact with a partial circuit and completes the circuit. The circuit area is perpendicular to a magnetic field with $B = 0.15\, T$. If the resistance of the total circuit is $3\,\Omega$,the force needed to move the rod as indicated with a constant speed of $2\, ms^{-1}$ will be equal to:

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The loops have lengths $L$ or $2L$. All loops enter a magnetic field $\vec{B}$ with the same velocity $v$. Which of the following is correct?

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Two straight conducting rails form a right angle as shown below. $A$ conducting bar in contact with the rails starts at the vertex at time $t=0$ and moves with a constant velocity of $v=5 \ m \ s^{-1}$ along them. $A$ magnetic field with $B=0.1 \ T$ is directed out of the page. The absolute value of the emf induced in the circuit at time $t=4 \ s$ will be (in $V$)?

EasyTS EAMCET 2020

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An aircraft with a wingspan of $40 \text{ m}$ flies with a speed of $1080 \text{ km h}^{-1}$ in the eastward direction at a constant altitude in the northern hemisphere,where the vertical component of the earth's magnetic field is $1.75 \times 10^{-5} \text{ T}$. The emf developed between the tips of the wings is: (in $\text{ V}$)

EasyKCET 2015

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$A$ coil of mean area $500 \ cm^2$ and having $1000$ turns is held with its plane perpendicular to a uniform magnetic field of $0.4 \ G$. If the coil is turned through $180^{\circ}$ in $\frac{1}{10} \ s$,then the average induced emf is $(1 \ G = 10^{-4} \ T)$. (in $V$)

MediumAP EAMCET 2019

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The loops have lengths $L$ or $2L$. All loops enter a magnetic field $\vec{B}$ with the same velocity $v$. Which of the following is correct?

$A$ coil of mean area $500 \ cm^2$ and having $1000$ turns is held with its plane perpendicular to a uniform magnetic field of $0.4 \ G$. If the coil is turned through $180^{\circ}$ in $\frac{1}{10} \ s$,then the average induced emf is $(1 \ G = 10^{-4} \ T)$. (in $V$)

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