Electromagnetic Induction - Result Question 37

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

[1990]

(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

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Answer:

Correct Answer: 37. (c)

Solution:

(c) $e=\frac{d \phi}{d t} ; i=\frac{e}{R}=\frac{1}{R} \frac{d \phi}{d t}$

Total charge induced $=\int i d t=\int \frac{1}{R} \frac{d \phi}{d t} \cdot d t$

$ =\frac{1}{R} \int _{\phi_1}^{\phi_2} d \phi=\frac{1}{R}(\phi_2-\phi_1) $