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 \( \mu_r \)?
Show Hint
- It depends on the geometry of solenoid.
- It does not depend on geometry of solenoid.
- It depends on cross sectional area of solenoid.
- It depends on relative permeability of the medium.
The Correct Option is A, C, D
Solution and Explanation
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).
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