First slide

Motional EMF

Question

A metal rod of resistance 20 $Ω$ is fixed along a diameter of a conducting ring of radius 0.1m and lies on x-y plane. There is a magnetic field $\vec{B} = (50 T) \hat{k}$ . The ring rotates with an angular velocity w = 20 rad s-1 about its axis. An external resistance of 10 $Ω$ is connected across the center of the ring and rim. The current through external resistance is

Easy

A

$\frac{1}{4}$
B

$\frac{1}{2}$
C

$\frac{1}{3}$
D

zero

Solution

$\begin{array}{l} V = \frac{B ω r^{2}}{2} = 5 V o l t \\ i = \frac{V}{R_{1} + R_{2}} = \frac{1}{3} A \end{array}$

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