The figure below shows two circular regions R1 and R2 with r

The figure below shows two circular regions R_1 and R_2 with radii F_1 = 11.0 cm and F_2 = 27.0 cm. In R_1 there is a uniform magnetic field of magnitude B_1 = 50.0 mT into the page and R_2 there is a uniform magnetic field B_2 = 7.50 mT out of the page (ignore fringing). Both fields are decreasing at the rate 8.30 mT/s. Calculate the integral j E d, for each of the three dashed paths.

Solution

for path 1

integral E.ds = -d(phi/dt)

phi = B*A

integral E.ds = A1*dB1/dt

= pi*r1^2*dB1/dt = 3.14*0.11^2*(-8.3*10^-3

= -3.15*10^-4 V.

2. for path 2

integral E.ds = pi*r2^2*dB2/dt

= 3.14*0.27^2*(-8.3*10^-3)

= -1.89*10^-3 V

3. for path 3

integral E3.ds =

= integral E1.ds - integral E2.ds

= (-3.15*10^-4) - (-1.89*10^-3)

= 1.57*10^-3 V