Question

During a transcranial magnetic stimulation (TMS) treatment, a magnetic field, typically of magnitude 5.00 T5.00 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 80.0????s80.0μs . Assume that the magnetic field is uniform over a circular area of diameter 2.00×10−2 m2.00×10−2 m inside the brain. What is the magnitude of the average induced emf around this region of the brain during the treatment?

Answer 1

`\epsilon=19.63\ V`

Step-by-step explanation:

It is given that,

Initial magnetic field,
`B_i = 0`

Final magnetic field,
`B_f=5\ T`

Time,
`t=80\ \mu s=80* 10^(-6)\ s`

Diameter of circular path,
`d=2* 10^(-2)\ m`

Radius of circular path,
`r=10^(-2)\ m`

The induced emf around this region of the brain is given by :

`\epsilon=-(d\phi)/(dt)`

`\phi=BA`

`\epsilon=-(d(BA))/(dt)`

`\epsilon=-A(dB)/(dt)`

`\epsilon=-\pi r^2(dB)/(dt)`

`\epsilon=-\pi (10^(-2))^2(5-0)/(80* 10^(-6))`

`\epsilon=19.63\ V`

So, the magnitude of the average induced emf around this region of the brain during the treatment is 19.63 volt. Hence, this is the required solution.