Answer:
[tex]\epsilon=19.63\ V[/tex]
Explanation:
It is given that,
Initial magnetic field, [tex]B_i = 0[/tex]
Final magnetic field, [tex]B_f=5\ T[/tex]
Time, [tex]t=80\ \mu s=80\times 10^{-6}\ s[/tex]
Diameter of circular path, [tex]d=2\times 10^{-2}\ m[/tex]
Radius of circular path, [tex]r=10^{-2}\ m[/tex]
The induced emf around this region of the brain is given by :
[tex]\epsilon=-\dfrac{d\phi}{dt}[/tex]
[tex]\phi=BA[/tex]
[tex]\epsilon=-\dfrac{d(BA)}{dt}[/tex]
[tex]\epsilon=-A\dfrac{dB}{dt}[/tex]
[tex]\epsilon=-\pi r^2\dfrac{dB}{dt}[/tex]
[tex]\epsilon=-\pi (10^{-2})^2\dfrac{5-0}{80\times 10^{-6}}[/tex]
[tex]\epsilon=19.63\ V[/tex]
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.
