(A) The motional $emf$ induced in the rod is given by $\varepsilon = B \ell v$.Given: $B = 0.15\, T$,$\ell = 50\, cm = 0.5\, m$,$v = 2\, ms^{-1}$,and

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(A) The motional $emf$ induced in the rod is given by $\varepsilon = B \ell v$.Given: $B = 0.15\, T$,$\ell = 50\, cm = 0.5\, m$,$v = 2\, ms^{-1}$,and $R = 3\,\Omega$.The induced current in the circuit is $I = \frac{\varepsilon}{R} = \frac{B \ell v}{R}$.The magnetic force acting on the rod is $F = I \ell B = \left(\frac{B \ell v}{R}\right) \ell B = \frac{B^2 \ell^2 v}{R}$.Substituting the values:$F = \frac{(0.15)^2 \times (0.5)^2 \times 2}{3} = \frac{0.0225 \times 0.25 \times 2}{3} = \frac{0.01125}{3} = 0.00375\, N$.Thus,$F = 3.75 \times 10^{-3}\, N$.

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

Medium

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:

A
$3.75\times10^{-3}\, N$
B
$2.75\times10^{-3}\, N$
C
$6.57\times10^{-4}\, N$
D
$4.36\times10^{-4}\, N$

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Electromagnetic Induction

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Motional EMI (Induced Parameter)

The horizontal component of the earth's magnetic field at a place is $3 \times 10^{-4} \, T$ and the angle of dip is $53^\circ$. $A$ metal rod of length $0.25 \, m$ is placed in the north-south position and is moved at a constant speed of $10 \, cm/s$ towards the east. The emf induced in the rod will be ...... $\mu V$. (Given $\tan 53^\circ = 4/3$)

Medium

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$A$ conducting circular loop is placed in the $X-Y$ plane in the presence of a magnetic field $\overrightarrow{B} = (3t^3 \hat{j} + 3t^2 \hat{k})$ in $SI$ units. If the radius of the loop is $1 \ m$,the induced emf in the loop at time $t = 2 \ s$ is $n\pi \ V$. The value of $n$ is:

MediumJEE MAIN 2022

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$A$ metallic square loop $ABCD$ is moving in its own plane with velocity $v$ in a uniform magnetic field perpendicular to its plane as shown in the figure. An electric field is induced:

EasyIIT 2001

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$A$ 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 $\text{V}$)? $(\pi = 3.14)$

MediumJEE MAIN 2025

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

DifficultJEE MAIN 2024

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$A$ conducting circular loop is placed in the $X-Y$ plane in the presence of a magnetic field $\overrightarrow{B} = (3t^3 \hat{j} + 3t^2 \hat{k})$ in $SI$ units. If the radius of the loop is $1 \ m$,the induced emf in the loop at time $t = 2 \ s$ is $n\pi \ V$. The value of $n$ is:

$A$ metallic square loop $ABCD$ is moving in its own plane with velocity $v$ in a uniform magnetic field perpendicular to its plane as shown in the figure. An electric field is induced:

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

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