The figure below shows an N-turn rectangular coil of length a and width b enteri

Question

The figure below shows an N-turn rectangular coil of length a and width b entering a region of uniform magnetic field of magnitude Bout directed out of the page. The velocity of the coil is constant and is upward in the figure. The total resistance of the coil is R. What are the magnitude and direction of the magnetic force on the coil for the following? (Use any variable or symbol stated above along with the following as necessary: v.)

O O O O ut (a) when only a portion of the coil has entered the region with the field magnitude Fg = direction uBouA downward (b) when the coil is completely embedded in the field magnitude FB =10 direction The magnitude is zero. (c) as the coil begins to exit the region with the field magnitude Fg = direction ou downward

Explanation / Answer

A)dB/dt = bBv, so the induced current is
I =/R=(-dB/dt)/R
=bvBN/R
Where the sign indicates it is counterclockwise (against the changing flux direction). And the force on the leading wires is
F = IL×B = I ·Nb·Bˆi =[v(bBN)/R]NbB

F=-v(bBN)2/R
C) as coil exits the field

The situation here is the inverse of that in (a), so the induced emf is clockwise, but the current through the portion of loop in the
magnetic field is still up, so the force is unchanged.

F=-v(bBN)2/R

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