Question

A closely wound long solenoid of self-inductance L is cut into two identical solenoids. The value of self-inductance of each small solenoid will be ______.

Options

• `L/2`

• 2L

• 3L

• 4L

Answer 1

A closely wound long solenoid of self-inductance L is cut into two identical solenoids. The value of self-inductance of each small solenoid will be `bbunderline(L/2)`.

Explanation:

Self-inductance of a long solenoid depends on its physical parameters. Let’s analyze how cutting the solenoid affects its inductance.

For a long-distance solenoid:

L = µ₀n²Al

Where:

n = number of turns per unit length = `N/l`

N = total number of turns

A = cross-sectional area

l = length of solenoid

Substituting n = `N/l`:

L = `mu_0(N/l)^2 Al`

= `mu_0 (n^2 A)/l`

When cut into two identical solenoids:

Each small solenoid has length = `l/2`

Number of turns in each = `N/2`

Area A remains same

Inductance of each small solenoid:

L' = `mu_0 ((N//2)^2 A)/((l//2))`

= `mu_0 ((N^2//4 xx A))/(l//2)`

= `mu_0 (N^2A)/4 xx 2/l`

= `mu_0 (N^2 A)/(2 l)`

= `1/2(mu_0 (N^2A)/l)`

= `L/2`

∴ Each small solenoid has half the inductance of the original solenoid.