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Electricity and Magnetism

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Moderate

Faraday: Voltage Induced In Slider of a Circular Wire

EANDM-HGNNMY

A circular loop of conducting wire with radius $r_o$ is in a plane oriented perpendicular to the direction of a uniform constant magnetic field $B_o$. As shown in the accompanying figure, placed on this wire loop are two conducting sliders. One slider is fixed and the other is rotating counter-clockwise with an angular frequency of $\omega$ rad/sec.

What is the magnitude of the voltage measured between points 'a' and 'b'? (assume points 'a' and 'b' are very close together at the center of the loop)

A

$V=B_o \omega \, r_o ^2$

B

$V=\cfrac{ B_o \omega \, \theta \, r_o ^2}{2}$

C

$V=\cfrac{ B_o \omega \, r_o ^2}{2}$

D

$V=B_o \omega \, r_o $