(D) The induced $e.m.f.$ $(e)$ in a conductor of length $l$ rotating about one end in a magnetic field $B$ with angular velocity $\omega$ is given by

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(D) The induced $e.m.f.$ $(e)$ in a conductor of length $l$ rotating about one end in a magnetic field $B$ with angular velocity $\omega$ is given by the formula: $e = \frac{1}{2} B \omega l^2$ Given: $l = 1\;m$ $\omega = 5\;rad/s$ $B = 0.2 \times 10^{-4}\;T$ Substituting these values into the formula: $e = \frac{1}{2} \times (0.2 \times 10^{-4}) \times 5 \times (1)^2$ $e = 0.1 \times 10^{-4} \times 5$ $e = 0.5 \times 10^{-4}\;V$ $e = 50 \times 10^{-6}\;V = 50\;\mu V$ Therefore,the correct option is $D$.

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

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$A$ metal conductor of length $1\;m$ rotates vertically about one of its ends at an angular velocity of $5\;rad/s$. If the horizontal component of the Earth's magnetic field is $0.2 \times 10^{-4}\;T$,then the $e.m.f.$ developed between the two ends of the conductor is:

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A
$5\;mV$
B
$5 \times 10^{-4}\;V$
C
$50\;mV$
D
$50\;\mu V$

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Motional EMI (Induced Parameter)

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$A$ metal conductor of length $1\;m$ rotates vertically about one of its ends at an angular velocity of $5\;rad/s$. If the horizontal component of the Earth's magnetic field is $0.2 \times 10^{-4}\;T$,then the $e.m.f.$ developed between the two ends of the conductor is:

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$A$ metal disc rotates freely between the poles of a magnet in the direction indicated. Brushes $P$ and $Q$ make contact with the center (axle) and the edge of the disc,respectively. What current,if any,flows through $R$?

$A$ rectangular metallic loop is moving out of a uniform magnetic field region to a field-free region with a constant speed. When the loop is partially inside the magnetic field,the plot of the magnitude of induced $\text{emf} \ (\varepsilon)$ with time $(t)$ is given by:

$A$ wire of length $L$ having resistance $R$ falls from a height $\ell$ in the Earth's horizontal magnetic field $B$. The induced emf through the wire is ($g$ = acceleration due to gravity).

$A$ long solenoid with $2000$ turns per meter has a small loop of radius $3 \,cm$ placed inside the solenoid normal to its axis. If the current through the solenoid increases steadily from $1.5 \,A$ to $5.5 \,A$ in $\frac{\pi^2}{100} \,s$, the induced emf in the loop is (in $\,mV$)

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