Question

If the number of turns per unit length of a coil of solenoid is doubled, the self-inductance of the solenoid will

A. remain unchanged
B. be halved
C. be doubled
D. become four times  
Answer :   become four times
Solution :
A long solenoid is that whose length is very large as compared to its radius of cross-section. If $$N$$ is total number of turns in the solenoid, $$A$$ is area of each turn of the solenoid and $$l$$ is length of solenoid, then self-inductance of solenoid is given by
$$\eqalign{ & L = \frac{{{\mu _0}{N^2}A}}{l} \Rightarrow L = {\mu _0}{n^2}Al\,\,\,\left( {n = {\text{number of turns per unit length}}} \right) \cr & So,\,\,L \propto {n^2} \cr} $$
When $${n^2}$$ is doubled, $$L$$ becomes 4 times.

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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