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JIPMER 2016
Exam
JIPMER
Year
2016
Subject
Physics
Chapter
Magnetic Properties of Matter

JIPMER 2016 · Physics · Magnetic Properties of Matter

The total charge induced in a conducting loop when it is moved in...

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

Options

  1. Athe rate of change of magnetic flux
  2. Binitial magnetic flux only
  3. Cthe total change in magnetic flux
  4. Dfinal magnetic flux only

Correct answer

C. the total change in magnetic flux

Step-by-step solution

Induced emf is given by e=−dϕdte=-\frac{d \phi}{d t} As, i=eR=−1Rdϕdt∴\quad i=\frac{e}{R}=-\frac{1}{R} \frac{d \phi}{d t} \therefore Total charge induced =∫idt=\int i d t=−∫1Rdϕdtdt=−1R∫ϕ1ϕ2dϕ=1R∫ϕ1ϕ2dϕ=1R(ϕ1−ϕ2)\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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