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

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(B) The induced emf $(e)$ 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:Length $l = 1 \; m$Angular velocity $\omega = 5 \; rad/s$Horizontal component of Earth's magnetic field $B_H = 0.2 \times 10^{-4} \; T$Substituting the values into the formula:$e = \frac{0.2 \times 10^{-4} \times 5 \times (1)^2}{2}$$e = \frac{1.0 \times 10^{-4}}{2}$$e = 0.5 \times 10^{-4} \; V$$e = 50 \times 10^{-6} \; V = 50 \; \mu V$Thus,the induced emf is $50 \; \mu V$.

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

Medium

$A$ metallic conductor of length $1 \; m$ rotates in a vertical plane parallel to the east-west direction about one of its ends with 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 emf induced between the two ends of the conductor is .............

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A
$5 \; \mu V$
B
$50 \; \mu V$
C
$5 \; mV$
D
$50 \; mV$

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Motional EMI (Induced Parameter)

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$A$ square loop $ABCD$ is moving with constant velocity $\vec{v}$ in a uniform magnetic field $\vec{B}$ which is perpendicular to the plane of paper and directed outward. The resistance of the coil is $R$. What is the rate of production of heat energy in the loop? [$L$ = length of side of the loop]

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