A square wire loop of dimensions L X L (L = 14.0 cm ) oriented in the xy-plane a

Question

A square wire loop of dimensions L X L (L = 14.0 cm) oriented in the xy-plane and centered on the x-axis enters a region where the magnetic field (B = 0.875 T) is first oriented in the +z- and then in the -z-direction. (Note: W = 14.001 cm and the magnetic field is zero outside the shaded area.) The loop moves at speed v = 7.45 ms  in the +x-direction. In the questions that follow, when asked for the emf, a positive emf will be defined as an emf induced counterclockwise (if viewed from above the loop); and vice versa.

What is the induced emf in the loop when the center of the loop is at x = -W?

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What is the induced emf in the loop when the center of the loop is at the origin?

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What is the induced emf in the loop when the center of the loop is at x = +W?

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Explanation / Answer

induced emf e = - d(phi)./dt

and flux phi = integral B.dA

whn the loop is at W/2 . loop will be completly inside

phi = B.A

at Oriing this remains constant so induced emf at origin = 0 (x = W/2) (answer to part B)

now for x = +W,

induced emf e -= -LBV

emf e = 0.14 * 0.875* 7.45

emf e = -0.912 Volts
-

at x = -W

emf e = +0.912 Volts

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