(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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Class 12

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Chapter

Electromagnetic Induction

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Motional EMI (Induced Parameter)

Derive the equation for the induced $emf$ in a rod of length $l$ sliding with velocity $v$ on a $U$-shaped frame placed perpendicular to a uniform magnetic field $B$.

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$A$ rod of length $60 \ cm$ rotates with a uniform angular velocity $20 \ rad \ s^{-1}$ about its perpendicular bisector in a uniform magnetic field of $0.5 \ T$. The direction of the magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is . . . . . . $V$.

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In a region where the Earth's magnetic field is $3 \times 10^{-4} \, T$ with a dip angle $\theta = \tan^{-1}(4/3)$,a metal rod of length $0.25 \, m$ is placed in the North-South direction. If it is moved towards the East with a velocity of $10 \, cm/s$,calculate the induced $emf$ in $\mu V$.

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$A$ conducting rod of length $l$ moves with a constant velocity $\upsilon$ perpendicular to a long,straight wire carrying a current $I$,as shown in the figure. Calculate the $emf$ generated between the ends of the rod.

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The figure shows four wire loops,with edge lengths of either $L$ or $2L$. All four loops move through a region of uniform magnetic field (directed out of the page) at the same constant velocity. Rank the four loops according to the maximum magnitude of the electromotive force (e.m.f.) induced as they move through the field,greatest first.

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Derive the equation for the induced $emf$ in a rod of length $l$ sliding with velocity $v$ on a $U$-shaped frame placed perpendicular to a uniform magnetic field $B$.

In a region where the Earth's magnetic field is $3 \times 10^{-4} \, T$ with a dip angle $\theta = \tan^{-1}(4/3)$,a metal rod of length $0.25 \, m$ is placed in the North-South direction. If it is moved towards the East with a velocity of $10 \, cm/s$,calculate the induced $emf$ in $\mu V$.

$A$ conducting rod of length $l$ moves with a constant velocity $\upsilon$ perpendicular to a long,straight wire carrying a current $I$,as shown in the figure. Calculate the $emf$ generated between the ends of the rod.

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