Question

Which of the following statements is/are CORRECT regarding self-inductance of a long solenoid having cross sectional area \( A \), length \( l \), and having \( n \) turns per unit length filled with material of relative permeability \( \mu_r \)?

• A. It depends on the geometry of solenoid.
• B. It does not depend on geometry of solenoid.
• C. It depends on cross sectional area of solenoid.
• D. It depends on relative permeability of the medium.

Hint:

The self-inductance of a solenoid is proportional to the cross-sectional area and the relative permeability of the medium.

Answer 1

The Correct Option is A, C, D

Step 1: Understanding self-inductance of a solenoid. 
The self-inductance \( L \) of a solenoid is given by the formula: \[ L = \frac{\mu_0 \mu_r n^2 A l}{l} \] where: - \( \mu_0 \) is the permeability of free space, - \( \mu_r \) is the relative permeability of the medium, - \( n \) is the number of turns per unit length, - \( A \) is the cross-sectional area, and - \( l \) is the length of the solenoid. From this formula, we see that \( L \) depends on the cross-sectional area \( A \) and the relative permeability \( \mu_r \), but does not depend on the geometry of the solenoid beyond the area. Additionally, the inductance is independent of the length \( l \) since it cancels out in the formula.

Step 2: Analyzing the options. 
(A) It depends on the geometry of solenoid: Correct — The inductance depends on the cross-sectional area \( A \), and so on the geometry. 
(B) It does not depend on geometry of solenoid: Incorrect — It depends on the cross-sectional area \( A \). 
(C) It depends on cross-sectional area of solenoid: Correct — The inductance depends on the cross-sectional area \( A \) of the solenoid. 
(D) It depends on relative permeability of the medium: Correct — The inductance depends on the relative permeability \( \mu_r \) of the medium inside the solenoid. 
 

Step 3: Conclusion. 
The correct answers are (A), (C) and (D).