A solenoid is a coil of wire that generates a magnetic field when an electric current is passed through it. The self-inductance of a solenoid is a measure of its ability to store energy in the magnetic field produced by it. It depends on various factors such as the number of turns, the cross-sectional area, and the length of the solenoid.


The self-inductance of a solenoid is directly proportional to the square of the number of turns and the cross-sectional area, and inversely proportional to the length of the solenoid. Thus, if the length of the solenoid is doubled while keeping the turn density and area constant, the self-inductance of the solenoid will decrease by a factor of 4.


The self-inductance of a solenoid can be calculated using the formula L = μ0n^2A/l, where L is the self-inductance, μ0 is the permeability of free space, n is the number of turns per unit length, A is the cross-sectional area, and l is the length of the solenoid.

If the length of the solenoid is doubled while keeping the turn density and area constant, the new length will be 2l, and the new self-inductance can be calculated using the same formula as L' = μ0n^2A/(2l).

Substituting the value of L in terms of L' in the above equation, we get L' = L/4. Thus, the new self-inductance of the solenoid will be 1/4th of the original self-inductance.


In conclusion, the self-inductance of a solenoid is inversely proportional to its length, and doubling the length of the solenoid while keeping the turn density and area constant will result in a decrease in the self-inductance by a factor of 4. This effect can be explained using the formula for self-inductance of a solenoid.