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. 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 be sufficient to stimulate neuronal activity. One such device generates a magnetic field within the brain that rises from zero to 1.5 T in 100 ms. Determine the magnitude of the induced emf within a circle of tissue of radius 1.0 mm and that is perpendicular to the direction of the field. epsilon = Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. mV

Explanation / Answer

1)Given that,

B1 = 0 T to B2 = 1.5 T in t = 100 ms = 0.1 s

radius = 1 mm = 0.001 m

Area = pi (0.001)2 = 3.14 x 10^-6 m^2

We know that, the flux is given as:

flux = phi = B A

So, phi1 = B1 A = 0 x 3.14 x 10^-6 m^2 = 0 Weber

2 = B2 A = 1.5 x 3.14 x 10^-6 m^2 = 4.71 x 10^-6 Weber.

We know from Faraday's Law that,

e = -d(phi) /dt = - ( phi1 - 2phi)/ t = -(0 - 4.71 x 10^-6 )/0.1 = 47.1 x 10^-6 V

Hence, the induced emf = e = 47.1 x 10^-6 V = 47.1 micro-V = 0.0471 milli-V.

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