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 that have a coil of very fine wire circling the edge. A current is induced in the coil each time the subject rotates his eye. Consider an experiment in which a 20-turn, 6.0 mm diameter coil of wire circles the subject's cornea while a 1.1 T magnetic field is directed as shown in the figure below. The subject begins by looking straight ahead. What emf is induced in the coil if the subject shifts his gaze by 8? in 0.20 s?

Explanation / Answer

emf induced in the coil , e = - d@/ dt

@ = magnetic flux= B.A = BA cos ( theta)

Here angle is changing.so

@ = B*A * [ cos ( thetafinal ) - cos( thetainitial)]          -----------------------------------1                

Here cos ( thetainitial ) = 900 because axis of coil is perpendicular to magnetic field as shown in fig.

cos ( thetafinal ) = 820 ( because subject shift his gaze by 80 means that changing his angle by 80 )

So from eq. 1

@ = B*A * [ cos ( 82) - cos ( 90) ]                                      ( A = pie*r2 = pie* ( d/2)2 = 2.82*10-5 m2 )

= 1.1*2.82*10-5 [ cos(82) - 0]

= 4.317*10-6   Wb

emf will be,        e = N d@/ dt                         ( N = no of turns)

e = 20*4.317*10-6 / 0.20

e = 4.317*10-4 volt

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