Question

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

The total change in magnetic flux

Induced emf is given by
$e=-\frac{d\varphi }{dt}$
As, $i=\frac{e}{R}=-\frac{1}{R}\frac{d\varphi }{dt}$
$\therefore$ Total charge induced $=\int idt$
$=-\int \frac{1}{R}\frac{d\varphi }{dt}dt=-\frac{1}{R}{\int }_{{\varphi }_1}^{{\varphi }_2}d\varphi$
$=\frac{1}{R}{\int }_{{\varphi }_1}^{{\varphi }_2}d\varphi =\frac{1}{R}({\varphi }_1-{\varphi }_2)$
Thus, the induced charge in a conducting loop, moving in a magnetic field depends on the total charge in magnetic flux.