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The total charge induced in a conducting loop when it is moved in magnetic field depends on
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The correct answer is:
the total change in magnetic flux
Induced emf is given by
$e=-\frac{d \phi}{d t}$
As, $\quad i=\frac{e}{R}=-\frac{1}{R} \frac{d \phi}{d t}$
$\therefore$ Total charge induced $=\int i d t$
$\begin{aligned} & =-\int \frac{1}{R} \frac{d \phi}{d t} d t=-\frac{1}{R} \int_{\phi_1}^{\phi_2} d \phi \\ & =\frac{1}{R} \int_{\phi_1}^{\phi_2} d \phi=\frac{1}{R}\left(\phi_1-\phi_2\right)\end{aligned}$
Thus, the induced charge in a conducting loop, moving in a magnetic field depends on the total change in magnetic flux.
$e=-\frac{d \phi}{d t}$
As, $\quad i=\frac{e}{R}=-\frac{1}{R} \frac{d \phi}{d t}$
$\therefore$ Total charge induced $=\int i d t$
$\begin{aligned} & =-\int \frac{1}{R} \frac{d \phi}{d t} d t=-\frac{1}{R} \int_{\phi_1}^{\phi_2} d \phi \\ & =\frac{1}{R} \int_{\phi_1}^{\phi_2} d \phi=\frac{1}{R}\left(\phi_1-\phi_2\right)\end{aligned}$
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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