Question

A coil of resistance $$400\,\Omega $$  is placed in a magnetic field. If the magnetic flux $$\phi \left( {Wb} \right)$$  linked with the coil varies with time $$t$$ (second) as $$\phi = 50\,{t^2} + 4.$$
The current in the coil at $$t = 2\,s$$  is

A. $$0.5\,A$$  
B. $$0.1\,A$$
C. $$2\,A$$
D. $$1\,A$$
Answer :   $$0.5\,A$$
Solution :
Induced emf in a coil is given by
$$E = \left| { - \frac{{d\phi }}{{dt}}} \right|$$
Given, $$\phi = 50\,{t^2} + 4\,$$
and resistance, $$R = 400\,\Omega $$
So, $$E = {\left| { - \frac{{d\phi }}{{dt}}} \right|_{t = 2}} = {\left| {100\,t} \right|_{t = 2}} = 200\,V$$
So, current in the coil will be
$$I = \frac{E}{R} = \frac{{200}}{{400}} = \frac{1}{2} = 0.5\,A$$

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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