Introduction:
Solenoids are long, cylindrical coils of wire that are used to generate a magnetic field when an electric current is passed through them. They are commonly used in a variety of applications such as electromagnets, inductors, and relays. The self-inductance of a solenoid is a measure of the ability of the solenoid to generate an electromotive force (EMF) in response to a change in the current flowing through it.

Given:
Self-inductance of the solenoid = 2 H

Effect of Length on Self-Inductance:
The self-inductance of a solenoid is directly proportional to its length. Therefore, if the length of the solenoid is doubled, the self-inductance of the solenoid will also double.

Effect of Turn Density and Area on Self-Inductance:
Turn density refers to the number of turns of wire per unit length of the solenoid. Area refers to the cross-sectional area of the solenoid. Both turn density and area affect the self-inductance of the solenoid.

- Turn Density: If the turn density is increased, i.e., more turns of wire are added per unit length, the self-inductance of the solenoid will increase. Conversely, if the turn density is decreased, the self-inductance will decrease.
- Area: If the cross-sectional area of the solenoid is increased, the self-inductance will increase. Similarly, if the area is decreased, the self-inductance will decrease.

Effect of Doubling the Length:
When the length of the solenoid is doubled while keeping the turn density and area constant, the self-inductance of the solenoid will double. This is because the self-inductance is directly proportional to the length of the solenoid.

Explanation:
Since the length of the solenoid is doubled, the new self-inductance will be twice the original self-inductance. Therefore, the new self-inductance will be 4 H (2 H * 2).

In summary, when the length of a solenoid is doubled while keeping the turn density and area constant, the self-inductance of the solenoid will double.