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 20 turn, 6.0 a-mm-diameter coil of wire circles the subject's cornea while a 0.90 T magnetic field is directed as shown in the figure. The subject begins by looking straight ahead.

What emf is induced in the coil if the subject shifts his gaze by 5.0 degrees in 0.30 seconds ?

Express your answer using two significant figures.

Explanation / Answer

Number of turns: n = 20,
Turns per-unit length: N = n/2r = 20/2*3x10-³
magnetic flux density: B = µoNI = 2 T

By Faraday's law of induction:

emf = Bv

angular velocity of shifting eye: = /t = 5°(/180°)/0.3 = 0.29 rad/s

linear velocity of shifting eye: v = r = (3x10-³)0.29 = 0.87x10-³ m/s

length of centerline path of toroid: = 2r = 2*3x10-³ = 18.8x10-³ m

emf = 0.9*18.8x10-³*0.87x10-³ = 14.7204 x10-6 volts

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