Experiments to study vision often need to track the movements of a subject\'s ey

Question

Experiments to study vision often need to track the movements of a subject's eye. One way of doing so is to have the subject sit in a magnetic field while wearing special contact lenses with a coil of very fine wire circling the edge. A current is induced in the coil each time the subject rotates his eye. Consider the experiment shown in the figure in which a 24-turn, 6.0-mm-diameter coil of wire circles the subject's cornea while a 1.2 T magnetic field is directed as shown. The subject begins by looking straight ahead.

What emf is induced in the coil if the subject shifts his gaze by 6 ? in 0.24 s ?

Explanation / Answer

d = 6mm , r = 3mm ,B =1.2 T, N =24 turns, t =0.24s

theta1 = 90degrees

theta2 = 6degrees

Electric flux phi = NBAcos(theta)

Induced emf e = -d(phi)/dt = [NBAcos(90) -NBAcos(6)]/t

e = -NB(pi*r2)cos(6)/t

e = [24*1.2*3.14*(3*10-3)2 *cos(6)]/(0.24)

e = 33.84x10-4 V

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