Question

If the number of turns in a solenoid is doubled keeping the other factors constant then what will be the new self inductance of the solenoid?

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

Answer 1

The correct option is D become four times

Magnetic field inside a solenoid with $n$ turns per unit length $={\mu }_{0}nI$.

Thus, flux inside the solenoid $=B\left(nl\right)A=B\left(nl\right)\pi r^2={\mu }_0{n}^{2}Il\pi r^2$

where, $\left(nl\right)$ are the total number of turns in the solenoid.

Thus, the self inductance of the solenoid $=L={\mu }_0{n}^2\pi r^{2}l$

As $n$ doubles, $L$ becomes four times.