During a transcranial magnetic stimulation (TMS) treatment, a magnetic field, typically of magnitude 5.00 T , is produced in the brain using external coils. During the treatment, the current in the coils (and hence the magnetic field in the brain) rises from zero to its peak in about 75.0 μ s . Assume that the magnetic field is uniform over a circular area of diameter 2.00 × 10 − 2 m inside the brain. What is the magnitude of the average induced emf around this region of the brain during the treatment?

20.9 V

Explanation:

Parameters given:

Magnetic field, B = 5.00 T

Time interval, t = 75 * 10^(-6) s

Diameter of coil = 2 * 10^(-2) m

Radius of coil, r = 1 * 10^(-2) = 0.01 m

The magnitude of the average induced EMF in the region of radius, r, due to the presence of a magnetic field, B, in a time interval, t, is given as:

EMF = | (-N*A*B) / t |

Where N = number of turns = 1 (in this case)

A = area of region = pi*r² = pi * 0.01²

EMF = | (-1 * pi * 0.01² * 5) / 75 * 10^(-6) |

EMF = 20.9 V

The magnitude of the average induced EMF around this region of the brain is 20.9 V