A circular loop of radius 21 cm is located in the plane of the paper inside a ho

Question

A circular loop of radius 21 cm is located in the plane of the paper inside a homogeneous magnetic field of 0.5 T pointing into the paper. It is connected in series with a resistor of 117 ?. The magnetic field is now increased at a constant rate by a factor of 2.6 in 21.0 s. Calculate the magnitude of the induced emf in the loop in V during that time. Calculate the current induced in the loop in A during that time. Calculate the average induced voltage, in V,  when the magnetic field is constant at 1.30 T while the loop is pulled horizontally out of the magnetic field region in 9.1 s at constant speed.

Explanation / Answer

r = 0.21 m

A = pi*r^2 = 0.138474 m^2
B = 0.5 T

R = 117 ohms


dB/dt = (2.6*0.5-0.5)/21 = 3.809*10^-2 T/s



induced emf = the rate of change of magnetic flux

emf = d(B*A)/dt

emf = A*dB/dt

emf = 0.138474*3.809*10^-2

emf = 5.274*10^-3 volts

i = emf/R = 4.508*10^-5 A

2)

B1 = 1.3 T
B2 = 0

t = 9.1 s

induced emf = A*(B2-B1)/t

emf = 0.138474*(0-1.3)/9.1

emf = 1.982*10^-2 volts

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