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Q.

The self inductance of a long solenoid of length $l$ is proportional to

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a

l^{2}

b

l

c

\frac{1}{l}

d

\frac{1}{l^{2}}

answer is C.

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Detailed Solution

The self inductance of a long solenoid of length

l

is proportional to

\frac{1}{l}

.
Whenever the electric current is passing through a coil changes, the magnetic flux linked with it will also change. As a result, by Faraday’s laws of electromagnetic induction, an emf is induced in the coil, which opposes the change that causes it. This phenomenon is called self-inductance, and the emf induced is called back emf, current so produced in the coil is called induced current.
Self-inductance of a solenoid is

L = \frac{μ_{0} N^{2} A}{l}

Where

μ_{0} =

Absolute permeability

N =

Number of turns

l =

length of the solenoid

A =

cross-sectional area of the solenoid
Thus we can say that

L α \frac{1}{l}

.

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