A 147-turn circular coil of radius 2.57 cm is immersed in a uniform magnetic fie

Question

A 147-turn circular coil of radius 2.57 cm is immersed in a uniform magnetic field that is perpendicular to the plane of the coil. During 0.175 s the magnetic field strength increases from 55.9 mT to 93.3 mT. Find the magnitude of the average EMF, in millivolts, that is induced in the coil during this time interval. A 123-turn circular coil of radius 3.45 cm and negligible resistance is immersed in a uniform magnetic field that is perpendicular to the plane of the coil. The cod is connected to a 13.5- ohm resistor to create a closed circuit. During a time interval of 0.193 s the magnetic field strength decreases uniformly from 0.517 T to zero. Find the energy, in millijoules, that is dissipated in the resistor during this time interval.

Explanation / Answer

a)E = N*(d/dt)

N*d = 147*pi*.0257^2 * (93.3 - 55.9)*10^-3

N*d = 11.407 mWb

dt = .175 s

E = 11.407/.175 = 65.183 mV

b) E = N*(d/dt)

i = E/R;

P = E*i

dB/dt = 0 - 0.517/.193 = 2.6787 T/s

P = (N*A*dB.dt)*(N*A*dB.dt)/R

P = (123*pi*.0345^2 *2.6787)^2/13.5

Power = .1124 W

energy = power * time = .1124 * .193 = .021699 J

energy dissipated = 21.699 mJ

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