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
Show Answer
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) $
