Transcranial magnetic stimulation (TMS) is a noninvasive technique used to stimu

Question

Transcranial magnetic stimulation (TMS) is a noninvasive technique used to stimulate regions of the human brain (see figure). In TMS, a small coil is placed on the scalp and a brief burst of current in the coil produces a rapidly changing magnetic field inside the brain. The induced emf can stimulate neuronal activity.

(a) One such device generates an upward magnetic field within the brain that rises from zero to 1.50 T in 130 ms. Determine the induced emf around a horizontal circle of tissue of radius 1.80 mm.

(b) The field next changes to 0.500 T downward in 90.0 ms. How does the emf induced in this process compare with that in part (a)?

magnitude     1 V direction     2---Select---clockwisecounterclockwise as seen from above Treatment Coil Prefrontal Cortex imulated Magneti Field

Explanation / Answer

(a)

Area of the circle of tissue with radius 1.8 mm is,

A = (3.14)(1.8X10-3 m)2

or, A = 1.02X10-5 m2, let the direction of area normal be upward

Now, initial magnetic field is B1 = 0

So initial flux is 1 = B1.A = 0

Final magnetic field is B2 = 1.5 T

So final flux is 2 = B2.A = (1.5 T)(1.02X10-5 m2) --------- (since B and A are both upward, B.A = BA)

So emf induced is E = -(2 - 1)/t = -(1.5 T)(1.02X10-5 m2)/130 ms = -(1.5 T)(1.02X10-5 m2)/0.13

or E = 1.17X10-4V

we assumed the area normal to be upward and the emf came out to be negative, so as seen from above the emf direction will be clockwise seen from above.

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(b)

Now, initial magnetic field is B2 = 1.5 T upward

So, initial flux is 2 = B2.A = (1.5 T)(1.02X10-5 m2) --------- (since B and A are both upward, B.A = BA)

final magnetic field is B3 = 0.5 T downward

So, final flux is, 3 = B3.A = -(0.5 T)(1.02X10-5 m2) ----------- (since B and A are opposite this time, B.A = -BA)

So emf induced is E = -(2 - 1)/t = -[-(0.5 T)(1.02X10-5 m2) - (1.5 T)(1.02X10-5 m2)]/0.09s

or, E = 2.26X10-4 V

Since the emf came to be positive, the direction will be counterclockwise as seen from above.

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