The total charge induced in a conducting loop when it is moved in magnetic field depends on

the rate of change of magnetic flux

initial magnetic flux only

the total change in magnetic flux

final magnetic flux only

Solution

the total change in magnetic flux

The induced emf is produced due to change in magnetic flux in the coil.

Induced emf is given by

e = $- \frac{dϕ}{dt}$

i = $\frac{e}{R}$

= $- \frac{1}{R} \frac{dϕ}{dt}$

∴ Total charge induced = $\int i dt$

= $- \int \frac{1}{R} \frac{dϕ}{dt}$ dt

= $- \frac{1}{R} \int_{ϕ_{1}}^{ϕ_{2}} dϕ$

= $\frac{1}{R} (ϕ_{1} - ϕ_{2})$

Thus, the induced charge in a conducting loop, moving in a magnetic field depends on the total change in magnetic flux.

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