Question

When a diamagnetic substance of relative permeability \(0.5\) is filled inside a solenoid, then its self-inductance

• A. becomes doubled
• B. becomes half
• C. is quadrupled
• D. becomes one-fourth

Hint:

The self-inductance of a solenoid depends on the permeability of the core. If a material with relative permeability \( \mu_r \) is inserted, the inductance changes as: \[ L' = \mu_r L_0 \] For diamagnetic materials, \( \mu_r<1 \), reducing the inductance.

Answer 1

The Correct Option is B

Step 1: Understanding the Formula for Self-Inductance The self-inductance \( L \) of a solenoid is given by: \[ L = \mu_r \mu_0 \frac{N^2 A}{l} \] where: 
- \( \mu_r \) is the relative permeability of the core material, 
- \( \mu_0 \) is the permeability of free space, 
- \( N \) is the number of turns, 
- \( A \) is the cross-sectional area, 
- \( l \) is the length of the solenoid. 

Step 2: Effect of Changing the Core Material If the solenoid is initially empty (air core), the self-inductance is: \[ L_0 = \mu_0 \frac{N^2 A}{l} \] When a diamagnetic material with relative permeability \( \mu_r = 0.5 \) is inserted, the new inductance becomes: \[ L' = 0.5 \times L_0 \] This shows that the self-inductance is reduced to half of its original value. Thus, the correct answer is \( \mathbf{(2)} \) becomes half.