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 1.0 T in 100 ms. Determine the magnitude of the induced emf within a circle of tissue of radius 1.6 mm and that is perpendicular to the direction of the field.

To give a solution to the exercise, it is necessary to consider the concepts related to magnetic flux and Faraday's law of induction. Faraday's law states that the voltage induced in a closed circuit is directly proportional to the speed with which the magnetic flux that crosses any surface with the circuit as an edge changes over time.

It is represented under the equation,

[tex]\epsilon = N \frac{\Delta\Phi}{\Delta t}[/tex]

Where,

[tex]\epsilon[/tex]is the induced electromotive force

N = Number of loops

[tex]\Delta t[/tex]= Time

[tex]\Delta\Phi[/tex]= Magnetic Flux

For definition the change in magnetic flux is:

[tex]\Delta \Phi = \Delta B A cos\phi[/tex]

Where,

B= Magnetic field

Substituting at the first equation we have

[tex]\epsilon = N \frac{\Delta B A Cos\phi}{\Delta t}[/tex]

[tex]\epsilon = N \frac{(B_2-B_1) (\pi r^2) Cos\phi}{\Delta t}[/tex]

Our values are given by,

N = 1 turn

[tex]B_2 = 1T[/tex]

[tex]B_1 = 0T[/tex]

r = 1.6mm

[tex]\phi = 0\°[/tex]

[tex]\Delta t = 100ms[/tex]

Replacing,

[tex]\epsilon = (1) \frac{(1-0) (\pi (1.6*10^{-3})^2) Cos(0)}{110*10^{-3}}[/tex]

[tex]\epsilon = 7.311*10^{-5}V[/tex]

Therefore the magnitud of the induced emf around a horizontal circle of tissue is [tex]7.3114*10^{-5}V[/tex]