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Electricity and Magnetism

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Faraday: Charge Flowing in a Conducting Wire in a Magnetic Field

EANDM-37PVUS

A circular loop of length $L_o$ is made of wire with cross-sectional area $a_o$. The wire has a resistivity of $\rho_o$. The loop is in a spatially uniform magnetic field. Initially, the loop is orientated such that the normal to its area is perpendicular to the direction of the magnetic field.

The loop is subsequently rotated $90^o$ to an orientation where the normal to its area is parallel to the magnetic field direction. During the time the loop is rotating, and charge of $Q_o$ flows in the wire.

What is the magnitude of the magnetic field in which the loop is placed?

A

$B = 2 \pi L_o Q_o \rho a_o $

B

$B = \cfrac{ Q_o }{\rho a_o L_o}$

C

$B = \cfrac{ Q_o \rho a_o }{L_o ^2}$

D

$B = \cfrac{ 4 \pi Q_o \rho a_o }{L_o}$