Question

By what factor is the self-inductance of an air solenoid changed if its length and number of coil turns are both tripled

Answer 1

The new self inductance is 3 times of the initial self inductance.

Step-by-step explanation:

The self inductance of a solenoid is given by :

`L=(\mu_oN^2 A)/(L)`

Where

N is number of turns per unit length

A is area of cross section

l is length of solenoid

If length and number of coil turns are both tripled,

l' = 3l and N' = 3N

New self inductance is given by :

`L'=(\mu_oN'^2 A)/(L')\\\\=(\mu_o(3N)^2 A)/(3L)\\\\=3(\mu_oN^2 A)/(L)\\\\=3L`

So, the new self inductance is 3 times of the initial self inductance.