First slide

Magnetic flux and induced emf

Question

In a region, there exist a uniform magnetic field $B_{0}$ along positive x-axis . A metallic wire of length 2a and one side along x-axis and one side parallel to y-axis is rotating about y-axis with an angular velocity $ω$ . Then at the instant shown, magnitude of induced electro motive force between $P and R$ is

Moderate

A

$B ω a^{2}$
B

$\frac{1}{2} B ω a^{2}$
C

$\frac{1}{4} B ω a^{2}$
D

zero

Solution

Electro motive force induced in the part $P Q$ is zero as $\vec{v} \times \vec{B}$ is zero and emf induced in part $Q R$ is $a \times a ω \times B = B ω a^{2} .$ Hence electro motive force induce in the rod $P R$ is $B ω a^{2}$

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