Question

If the number of turns per unit length of a coil of solenoid is doubled, the self-inductance of the solenoid will

• A. remain unchanged
• B. be halved
• C. be doubled
• D. become four times

Answer 1

The Correct Option is D

To understand how doubling the number of turns per unit length of a solenoid affects its self-inductance, we need to look at the formula for the self-inductance of a solenoid, which is given by:

L = \mu_0 \cdot n^2 \cdot A \cdot l

where:

• L is the self-inductance.
• \mu_0 is the permeability of free space.
• n is the number of turns per unit length of the coil.
• A is the cross-sectional area of the solenoid.
• l is the length of the solenoid.

From the formula, we observe that the self-inductance L is directly proportional to the square of the number of turns per unit length n^2:

L \propto n^2

Now, if the number of turns per unit length n is doubled, the effective number becomes 2n. Substituting this in the formula, we get:

L' = \mu_0 \cdot (2n)^2 \cdot A \cdot l = \mu_0 \cdot 4n^2 \cdot A \cdot l

This shows that the new self-inductance L' is four times the original self-inductance L:

L' = 4L

Thus, doubling the number of turns per unit length of a solenoid causes its self-inductance to become four times what it initially was.

Conclusion: The correct option is: become four times.