Question

A magnetic field of $$2 \times {10^{ - 2}}T$$   acts at right angles to a coil of area $$100\,c{m^2},$$  with 50 turns. The average emf induced in the coil is $$0.1\,V,$$  when it is removed from the field in $$t$$ second. The value of $$t$$ is

A. $$10\,s$$
B. $$0.1\,s$$  
C. $$0.01\,s$$
D. $$1\,s$$
Answer :   $$0.1\,s$$
Solution :
Emf induced in the coil due to change in magnetic flux
$$e = - \frac{{d\phi }}{{dt}} = - \frac{{\left( {{\phi _2} - {\phi _1}} \right)}}{{dt}}$$
When magnetic field is perpendicular to coil
$${\phi _1} = NBA$$
When coil is removed, $${\phi _2} = 0$$
So, $$e = - \frac{{\left( {0 - NBA} \right)}}{{dt}}\,\,{\text{or}}\,\,dt = \frac{{NBA}}{e}$$
Here, $$N = 50,B = 2 \times {10^{ - 2}}T,A = 100\,c{m^2}$$
$$\eqalign{ & = {10^{ - 2}}{m^2}\,{\text{and}}\,\,e = 0.1\,V \cr & \therefore dt = \frac{{50 \times 2 \times {{10}^{ - 2}} \times {{10}^{ - 2}}}}{{0.1}} \cr & = 0.1\,s \cr} $$

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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Electromagnetic Induction


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