Question

Prove that induced charge does not depend upon the rate of change of magnetic field .

Answer 1

Let us consider f is the magnetic flux.

So,

We know that,

Induced Emf is $E=\frac{-df}{dt}$

Since Current $I=\frac{E}{R}=\frac{-df}{dtR}....$ Where R is the resistance

Now,

$I=\frac{dq}{dt}....2$ Where q is the charge.

By equating the equation 1 and2 then we get,

$\frac{-df}{dtR}=\frac{dq}{dt}$

Elemenating $dt$ in both sides then we get,

$dq=\frac{-df}{R}$

Thus, We can say that induced charge does not depend on the rate of flux.