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 16-turn, 6.0-mm-diameter coil of wire circles the subject's cornea while a 1.3 T magnetic field is directed as shown. The subject begins by looking straight ahead.
(Figure 1)

Part A

What emf is induced in the coil if the subject shifts his gaze by 6 in 0.25 s ?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Diameter = 6.0 mm

so, radius r = 6/2 = 3.0 mm = 0.003 m.

As we know that, induced emf = rate of change of flux-linkage

Now in our case due to a change in the flux gathering area (dA/dt) perpendicular to the field.

dA/dt (per turn) = (6º/360º) x (0.003m)² / 0.25s = 1.88 x 10^-6 m²/s

E = nB.dA/dt

E = 16 x 1.3T x 1.88 x 10^-6 m²/s = 3.9 x 10^-5 V

So, the requisite induced emf in the coil = 3.9 x 10^-5 V

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