Question

The self inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases as ______.

Options

• l and A increase.

• l decreases and A increases.

• l increases and A decreases.

• both l and A decrease.

Answer 1

The self inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases as l decreases and A increases.

Explanation:

The self inductance L of a solenoid depends on various factor like geometry and magnetic permeability of the core material.

L = μ_rμ₀ N² Al

Where n = N/l (no. of turns per unit length)

1. No. of turns: Larger the number of turns in solenoid, larger is its self inductance.
2. Area of cross-section: Larger the area of cross-section of the solenoid, larger is its self inductance.
3. Permeability of the core material. The self inductance of a solenoid increases μr times if it is wound over an iron core of relative permeability μ_r.

The long solenoid of cross-sectional area A and length l, having A turns, filled inside of the solenoid with a material of relative permeability (e.g., soft iron, which has a high value of relative permeability) then its self inductance is L = μ_rμ₀ N² A/l

So, the self inductance L of a solenoid increases as l decreases and A increases because L is directly proportional to the area and inversely proportional to length.

Important point: The self and mutual inductance of capacitance and resistance depend on the geometry of the devices as well as permittivity/ permeability of the medium.