A current-carrying coil of total resistance R is kept inside magnetic field. How is the change in magnetic flux through the coil related to the amount of charge passing through the coil ?

Explanation

Let `Deltaphi` be the change in magnetic flux through the coil in time interval `Deltat`. Then average emf can be written as follows:
`epsilon_(av) = (Deltaphi)/(Deltat)`
Average current through the coil in this time interval can be written as follows:
`I_(av)=(e_(av))/(R)=(1)/(R)(Deltaphi)/(Deltat)`
Total charge circulated through the coil can be calculated as follows:
`Deltaq=I_(av)Deltat`
`Deltaq=(Deltaphi)/(R)`
Hence charge circulated through the coil is equal to change in magnetic flux divided by the resistance of the coil. Note that charge amount is independent of the time it takes to change the flux by given amount.