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
C. the total change in magnetic flux  
D. final magnetic flux
Answer :   the total change in magnetic flux
Solution :
Total charge induced in a conducting loop is $$q = \int i dt$$
As, $$i = \frac{e}{R}$$
$$\therefore q = \int {\frac{e}{R}} dt = \frac{1}{R}\int e dt$$
Induced emf $$e$$ is given by
$$\eqalign{ & e = - \frac{{d\phi }}{{dt}} \cr & \therefore q = \frac{1}{R}\int {\left( { - \frac{{d\phi }}{{dt}}} \right)dt} \cr & = \frac{1}{R}\int {d\phi } \cr} $$
Hence, total charge induced in the conducting loop depends upon resistance of loop and change in magnetic flux.

Releted MCQ Question on
Electrostatics and Magnetism >> Electromagnetic Induction

Releted Question 1

A thin circular ring of area $$A$$ is held perpendicular to a uniform magnetic field of induction $$B.$$ $$A$$ small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of the circuit is $$R.$$ When the ring is suddenly squeezed to zero area, the charge flowing through the galvanometer is

A. $$\frac{{BR}}{A}$$
B. $$\frac{{AB}}{R}$$
C. $$ABR$$
D. $$\frac{{{B^2}A}}{{{R^2}}}$$
Releted Question 2

A thin semi-circular conducting ring of radius $$R$$ is falling with its plane vertical in horizontal magnetic induction $$\overrightarrow B .$$  At the position $$MNQ$$  the speed of the ring is $$v,$$ and the potential difference developed across the ring is
Electromagnetic Induction mcq question image

A. zero
B. $$\frac{{Bv\pi {R^2}}}{2}$$  and $$M$$ is at higher potential
C. $$\pi RBv$$  and $$Q$$ is at higher potential
D. $$2RBv$$  and $$Q$$ is at higher potential
Releted Question 3

Two identical circular loops of metal wire are lying on a table without touching each other. Loop-$$A$$ carries a current which increases with time. In response, the loop-$$B$$

A. remains stationary
B. is attracted by the loop-$$A$$
C. is repelled by the loop-$$A$$
D. rotates about its $$CM,$$  with $$CM$$  fixed
Releted Question 4

A coil of inductance $$8.4 mH$$  and resistance $$6\,\Omega $$  is connected to a $$12 V$$  battery. The current in the coil is $$1.0 A$$  at approximately the time

A. $$500 s$$
B. $$25 s$$
C. $$35 ms$$
D. $$1 ms$$

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Electromagnetic Induction


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