Question

If flux in a coil changes by $\Delta$ $\varphi$, and the resistance of the coil is R, prove that the charge flown in the coil during the flux change is $\frac{\Delta \varphi }{R}$. (Note: It is independent of the time taken for the change in flux)

Answer 1

Flux in the coil changes by $△\varphi$

Resistance of coil $=R$

Now,

EMF $=-\frac{d\varphi }{dt}$ (from faradays law)

$\therefore V=-\frac{d\varphi }{dt}$

Also,

$I=\frac{dQ}{dt}=\frac{V}{R}$

$\Rightarrow \frac{dQ}{dt}=\frac{V}{R}$

$\{dQ=-\frac{d\varphi }{R}=-\frac{△\varphi }{R}\}$

Hence proved