Question 229: Electromagnetic Induction

Question

If number of turns per unit length in a solenoid is tripled, the self inductance of solenoid will

Accepted Answer

The self-inductance ($L$) of a solenoid is given by the formula:
$$ L = \frac{\mu_0 \cdot N^2 \cdot A}{l} $$
where:
$\mu_0$ is the permeability of free space,
$N$ is the total number of turns,
$A$ is the cross-sectional area,
$l$ is the length of the solenoid.
For the solenoid, the number of turns per unit length is represented by $n = \frac{N}{l}$. If the number of turns per unit length is tripled, represent this as $n' = 3n$. Therefore, the new number of turns $N' = n' \cdot l = 3n \cdot l = 3N$.
Substituting $N'$ into the original formula for self-inductance:
$$ L' = \frac{\mu_0 \cdot (3N)^2 \cdot A}{l} = \frac{\mu_0 \cdot 9N^2 \cdot A}{l} = 9 \cdot \frac{\mu_0 \cdot N^2 \cdot A}{l} $$
This demonstrates that the self-inductance will become 9 times greater if the number of turns per unit length is tripled.
Therefore, the correct answer is:
Option C: become 9 times

Answer

remain constant

Answer

be halved

Answer

become 9 times

Answer

become $\frac{1}{9}$ times

Electromagnetic Induction

If number of turns per unit length in a solenoid is tripled, the self inductance of solenoid will

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