(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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$A$ 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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$A$ conducting rod $PQ$ of length $L = 1.0 \, m$ is moving with a uniform speed $v = 2 \, m/s$ in a uniform magnetic field $B = 4.0 \, T$ directed into the paper. $A$ capacitor of capacity $C = 10 \, \mu F$ is connected as shown in the figure. Then:

$A$ metal rod of length $2 \, m$ is rotating with an angular velocity of $100 \, rad/s$ in a plane perpendicular to a uniform magnetic field of $0.3 \, T$. The potential difference between the ends of the rod is.......$V$

$A$ copper rod $AB$ of length $L$,pivoted at one end $A$,rotates at a constant angular velocity $\omega$,at right angles to a uniform magnetic field of induction $B$. The e.m.f. developed between the midpoint $C$ of the rod and end $B$ is

$A$ straight conductor of length $0.6 \, m$ is moved with a speed of $10 \, ms^{-1}$ perpendicular to a magnetic field of induction $1.2 \, Wb \cdot m^{-2}$. The induced e.m.f. across the conductor is (in $V$)

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