Question

If the number of turns of a solenoid is doubled keeping other factors constant, how does the self inductance of the soleniod change?

Answer 1

Given, number of turns of solenoid is double keeping all other factors constant.

Coefficient of self induction is given by,

L = μ0N^2A / l = L1

where

N is the number of turns of the solenoid

A is the area of each turn of coil

l is the length of the solenoid

and μ0 is the permeability constant



so, if the number of turns were to be doubled the self inductance would be

L2 = μ0 (2N)^2A / l

or

L2 = 4L1
Therefore, when number of turns is doubled, the coefficient of self induction will increase 4 times of it's initial value.