Question

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

• A. the rate of change of magnetic flux
• B. initial magnetic flux only
• C. the total change in magnetic flux
• D. final magnetic flux only

Answer 1

Answer: (C)

$q=\int idt=\frac{1}{R}\int \in dt=\left(\frac{-d\varphi }{dt}\right)\frac{1}{R}\int dt=\frac{1}{R}\int d\varphi$
Hence total charge induced in the conducting loop
depend upon the total change in magnetic flux.
As the emf or iR depends on rate of change of $\varphi$,
charge induced depends on change of flux.