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Electricity and Magnetism

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Moderate

Faraday's Law: Induced Current

EANDM-I33IKS

A loop of conducting 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. There is a resistor $R$ placed between points $a$ and $b$,. The magnetic field is changing in time according to:

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

What is the expression for the current $I(t) $ induced in the conducting loop? [Assume the points $a$ and $b$ are very close to one another]

A

$ I(t)=\cfrac{ \bigg(B_o \, \omega \,cos(\omega t ) \pi r^2\bigg)}{R} $

B

$ I(t)=\cfrac{ \bigg(B_o \, cos(\omega t ) \pi r^2\bigg)}{R} $

C

$ I(t)=\cfrac{ \bigg(B_o \, \omega \, sin(\omega t ) \pi r^2\bigg)}{R} $

D

$ I(t)=\cfrac{ \bigg(B_o \, \omega \,cos(\omega t ) \bigg)}{R} $