Question

A conducting circular loop made of a thin wire, has area $$3.5 \times {10^{ - 3}}{m^{ - 2}}$$     and resistance 10$$\Omega $$. It is placed perpendicular to a time dependent magnetic field $$B\left( t \right) = \left( {0.4T} \right)\sin \left( {50\pi t} \right).$$     The the net charge flowing through the loop during $$t= 0\,s$$  and $$t = 10\,ms$$   is close to:

A. $$0.14\,mC$$  
B. $$7\,mC$$
C. $$0.21\,mC$$
D. $$6\,mC$$
Answer :   $$0.14\,mC$$
Solution :
$$\eqalign{ & {\text{Net charge }}Q = \frac{{\Delta \phi }}{R} = \frac{1}{{10}}A\left( {{B_f} - {B_i}} \right) = \frac{1}{{10}} \times 3.5 \times {10^{ - 3}} \cr & \left( {0.4\sin \frac{\pi }{2} - 0} \right) \cr & = \frac{1}{{10}}\left( {3.5 \times {{10}^{ - 3}}} \right)\left( {0.4 - 0} \right) \cr & = 1.4 \times {10^{ - 4}} \cr & = 0.14\,mC \cr} $$

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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