Question

The magnetic flux $$\phi $$ linked with a conducting coil depends on time as $$\phi = 4{t^n} + 6,$$   where $$n$$ is a positive constant. The induced emf in the coil is $$e.$$ Then which is wrong?

A. If $$0 < n < 1,\,e \ne 0$$    and $$\left| e \right|$$ decreases with time
B. If $$n = 1,$$  $$e$$ is constant
C. If $$n > 1,\left| e \right|$$   increases with time
D. If $$n > 1,\left| e \right|$$   decreases with time  
Answer :   If $$n > 1,\left| e \right|$$   decreases with time
Solution :
$$\eqalign{ & \phi = 4{t^n} + 6 \cr & \frac{{d\phi }}{{dt}} = 4n{t^{n - 1}} \cr & \left| e \right| = 4n{t^{n - 1}},\left| e \right| = \frac{{4n}}{{{t^{1 - n}}}} \cr} $$

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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