Rate of decrease of the magnetic fields

[Oblakastouf]

Let V_B be the rate of decrease of the magnetic fields

\frac{dB}{dt}

For the 3rd path:
\oint E\cdot ds = -\frac{d\phi _B}{dt} = -\frac{{d\phi _B}_1 + {d\phi _B}_2}{dt}

\phi _B_{(t)} = A_{(t)}B_{(t)}
The area is constant, it's only the magnetic field that's changing:
\phi _B_{(t)} = \pi R^2(B_0 - V_Bt)

Since B1 and B2 are in opposite directions, give one of them a minus sign:
{\phi _B}_1 + {\phi _B}_2 = \pi R_1^2(B_0 - V_Bt) - \pi R_2^2(B_0 - V_Bt) = \pi (B_0 - V_Bt)(R_1^2 - R_2^2)
Take the derivative of that:
\frac{{d\phi _B}_1 + {d\phi _B}_2}{dt} = -\pi V_B(R_1^2 - R_2^2)

And therefore:
\oint E\cdot ds = \pi V_B(R_1^2 - R_2^2)

 

[Fizex]

We appreciate that you know latex, but the title is useless, and you didn't follow the template. You also don't describe the problem. Don't expect an answer.