Question
Asked Dec 23, 2019
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A rectangular coil with resistance R has N turns, each of length
,l and width w, as shown in Figure P20.55. The coil moves into
a uniform magnetic field B
with constant velocity v
. What
are the magnitude and direction of the total magnetic force
on the coil (a) as it enters the magnetic field, (b) as it moves
within the field, and (c) as it leaves the field?

х х х х х
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х х х х х
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х х х
х х
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х х х
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-e-
х х
х х х
х
х
Figure P20.55
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х х х х х х х х х х х х х х х х х х х х х х х х х х х х -e- х х х х х х х Figure P20.55

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Expert Answer

Step 1

Part A:

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Given Info: The magnetic flux and the magnetic field The right end of the coil has entered into the field, but the left end has not, the flux through the area enclosed by the coil is directed into the page. This increasing flux induced an emf as, (1) At e is the induced emf, APB/At is the rate of change of magnetic flux, Use NBA for p in the equation (1) NB(AA) (2) At NBwv Nis the number of turns, • Bis the magnetic field, • w is the width of the coil, v is the speed of the coil moving inside the field,

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Step 2
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This emf produces a counterclockwise current in the loop to oppose the inward flux. The magnitude of the induced current is, É (3) I : • Iis the induced current, • Ris the resistance of the coil, Use NBwv for e in the equation (3). I= NBwv %3D

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Step 3
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The field exerts a magnetic force of the magnitude is, F = NBIW (4) • Fis the magnetic force, Substitute equation (3) in equation (4). NBwv F = NB R N°B°u?v Therefore, the magnitude of the total magnetic force on the coil is F = N° B²w?v/R and the direction of the magnetic force pointed towards the left.

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Current Electricity

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