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Electricity and Magnetism

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Moderate

Farady's Law-Induced Voltage in a Loop of Wire

EANDM-PSFSUH

A loop of wire with radius $r$ is in a plane that is perpendicular to a spatially constant magnetic field. As shown in the accompanying figure, the magnetic field is pointed into the plane that contains the loop. The magnetic field is changing in time according to:

$$B(t)=B_o sin(wt)$$

What is the expression for the magnitude of the voltage difference $V(t)$ measured between points $a$ and $b$ on the figure? [Assume the points $a$ and $b$ are very close to one another]

A

$V(t)=B_o \, cos(\omega t ) \pi r^2 $

B

$V(t)=B_o \, \omega \, cos(\omega t ) $

C

$V(t)=B_o\pi r^2 $

D

$V(t)=B_o \, \omega \, cos(\omega t ) \pi r^2 $