Question

The inductance of a solenoid L having diameter d. Let n be the number of turns per unit length. The inductance per unit length near the middle of a solenoid is ______.

(Assume that, l = current passes through the turns, µ₀ = Permeability of vacuum)

विकल्प

• `(mu_0pin^2d)/2`

• `(mu_0pin^2d^2)/4`

• `(mu_0pind^2)/4`

• `(mu_0pin^2d^2)/2`

Answer 1

The inductance of a solenoid L having diameter d. Let n be the number of turns per unit length. The inductance per unit length near the middle of a solenoid is `underlinebb((mu_0pin^2d^2)/4)`.

Explanation:

The inductance of a solenoid is given by,

L = `(mu_0N^2A)/l = mu_0(N/l)^2 xx l xx pi xx d^2/4`

∴ Inductance per unit length,

`L/l = (mu_0pin^2d^2)/4                (∵ N/l = n)`