Question

A current of $$1.5\,A$$  flows through a solenoid of length $$20.0\,cm,$$  cross-section $$20.0\,c{m^2}$$  and 400 turns. The current is suddenly switched off in a short time of 1.0 millisecond. Ignoring the variation in the magnetic field the ends, the average back emf induced in the solenoid is:

A. $$0.3\,V$$  
B. $$9.6\,V$$
C. $$30.0\,V$$
D. $$3.0\,V$$
Answer :   $$0.3\,V$$
Solution :
$$\eqalign{ & {e_{{\text{back}}}} = L\frac{{di}}{{dt}} \cr & {\text{where}}\,L = \frac{{{\mu _0}{N^2}A}}{l} \cr & \therefore {e_{{\text{back}}}} = \frac{{{\mu _0}{N^2}A}}{l}\left[ {\frac{{1.5 - 0}}{{1 \times {{10}^3}}}} \right] \cr & = \frac{{4\pi \times {{10}^{ - 7}}{{\left( {400} \right)}^2} \times 20 \times {{10}^{ - 4}}}}{{20 \times {{10}^{ - 2}}}} \times \left( {1.5 \times {{10}^3}} \right) \cr & = 0.3\,V \cr} $$

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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