The dimensions of the rectangular loop of wire in(Figure 1) are = 90 mm and w =

Question

The dimensions of the rectangular loop of wire in(Figure 1) are = 90 mm and w = 80 mm . The loop moves at speed v = 30 mm/s through the magnetic field shown. The field magnitude increases linearly from Bi(xi) = 10 mT at xi = 300 mm toBf(xf) = 60 mT at xf = 900 mm. The area vector of the loop is parallel to the magnetic field direction.

What is the induced emf in the loop?

Express your answer with the appropriate units. Enter positive value if the emf causes clockwise induced current and negative value if the emf causes counterclockwise induced current.

Explanation / Answer

change in magnetic field, dB = 60mT - 10mT = 50 mT

dB = 50 x 10^-3 T

dt = distance / speed = (900 - 300)/30 = 20 sec

A = lw = 0.09 m x 0.08 m = 7.2 x 10^-3 m^2

induced emf = d(BA) / dt = A dB/dt

     = (7.2 x 10^-3 ) ( 50 x 10^-3) / (20)

     = 1.8 x 10^-5 volt

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