Question

MY NOTES

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 135 ms. Determine the induced emf around a horizontal circle of tissue of radius 2.00 mm.

magnitude	μV
direction	clockwise  as seen from above

(b) The field next changes to 0.500 T downward in 85.0 ms. How does the emf induced in this process compare with that in part (a)?

magnitude	μV
direction	counterclockwise  as seen from above

Answer 1

Solution:

Magnetic Field Within Brain rises from zero to 1.50 Tesla in 135 ms.

Radius of horizontal circle of tissue is 2.00 mm

So, r = 2.00 mm = 2*10^-3 meter, Area = Pi(r)^2 = 1.256*10^-5 m^2

Therefore, Induced Emf = - d/dt [B.A] = A.dB/dt = (1.256*10^-5)*{(1.50-0)/135*10^-3}

Therefore, Induced Emf = 139*10^-6 Volt = 139.56 micro Volt [Answer]

B) Now Field changes to 0.500 T downward in 85.0 ms

Therefore, Emf Induced = -d/dt [ BA] = dB/dt(A) = (0.500-1.50)/(85*10^-3) * (1.256*10^-5) = 147.76*10^-6 Volt = 147.76 micro Volt [Answer]