Show that if the flux of magnetic induction through a coil changes from `phi_(1)" to "phi_(2)` then the charge q that flows through the circuit of total resistance R is given by `q=(phi_(2)-phi_(1))/(R)` where R is the resistance of the coil.

Explanation

Let `phi` be the instantaneous flux. Then `(dphi)/(dt)` is the instantaneous rate of change of flux which is equal to the magnitude of the instantaneous emf. So the current in the circuit `|i|=(1)/(R)((dphi)/(dt))` , since the current is the rate of flow of charge, that is, `i=(dq)/(dt)`
`q=intidtorq=underset(t=0)overset(t=t)int((1)/(R).(dphi)/(dt))dt`
where `tau` is the time during which change takes place. but at `t=0, phi=phi_(1),` and at `t=t,phi=phi_(2)`
`:. `:.q=(1)/(R)underset(phi=phi_(1))overset(phi=phi_(2))intdphi=(phi_(2)-phi_(1))/(R)`