Transcranial magnetic stimulation (TMS) is a noninvasive method to stimulate the

Question

Transcranial magnetic stimulation (TMS) is a noninvasive method to stimulate the brain using magnetic fields. It is used in treating strokes, Parkinson’s disease, depression, and other physical conditions. In the procedure, a circular coil is placed on the side of the forehead to generate a magnetic field inside the brain. Although values can vary, a typical coil would be about 17 cm in diameter and contain 250 thin circular windings. The magnetic field in the cortex (3.0 cm from the coil measured along a line perpendicular to the coil at its center) is typically 0.50 T.

1) What current in the coil is needed to produce the desired magnetic field inside the brain? (Express your answer to two significant figures.)

2) What is the magnetic field at the center of the coil at the forehead? (Express your answer to two significant figures.)

Explanation / Answer

Here,

radius ,r = 17/2 = 8.5 cm

r = 0.085 m

number of coils , n = 250

x = 3 cm = 0.03 m

magnetic field , B = 0.50 T

a) let the current in the coil is I

magnetic field due to coil at the axis = N * 2pi * r^2 * I* u0/(4pi * (x^2 + r^2)^1.5)

magnetic field due to coil at the axis = 250 * 2pi * 0.085^2 * I* 4pi *10^-7/(4pi * (0.085^2 + 0.03^2)^1.5)

0.50 = 250 * 2pi * 0.085^2 * I* 4pi *10^-7/(4pi * (0.085^2 + 0.03^2)^1.5)

solving for I

I = 322.7 A

the current in the coil must be 322.7 A

b)

magnetic field at the centre = N * u0 * I/(2R)

magnetic field at the centre = 250 * 4pi *10^-7 * 322.7/(2 * 0.03)

magnetic field at the centre = 1.68 T

the magnetic field at the centre of the coil is 1.68 T

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