A circular loop of radius 31 cm is located in the plane of the paper inside a ho

Question

A circular loop of radius 31 cm is located in the plane of the paper inside a homogeneous magnetic field of 0.9 T pointing into the paper. It is connected in series with a resistor of 281 . The magnetic field is now increased at a constant rate by a factor of 2.3 in 23.0 s. a) Calculate the magnitude of the induced emf in the loop in V during that time.
b) Calculate the current induced in the loop in A during that time.
c) Calculate the average induced voltage, in V, when the magnetic field is constant at 2.07 T while the loop is pulled horizontally out of the magnetic field region in 1.1 s at constant speed.

Explanation / Answer

a) Induced EMF e = rate of change of flux = d(BA) / dt

e = A dB/dt   = ( pi R^2 ) dB/dt

e = ( pi x 0.31^2) ( 2.3 / 23)   = 0.0302 V

b) I = V / R = 0.0302 / 281   = 1.07 x 10^-4 A

c) now EMF e = B (dA /dt) = 2.07 x pi x 0.31^2 / 1.1 =0.568 V

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