Question

What will happen to the inductance of a solenoid when the number of turns and the length are doubled, keeping the area of cross-section same?

• A. $\frac{L}{2}$
• B. $L$
• C. $2L$
• D. $4L$

Answer 1

The correct option is C $2L$

Self inductance of long solenoid $L=\frac{{\mu }_o{N}^{2}A}{l}$

where $N,$ $A$ and $l$ represent the number of turns, cross-section area and length of solenoid respectively.

For $N^{\prime }=2N$, $l^{\prime }=2l$ $A^{\prime }=A$

$\therefore$ $L^{\prime }=\frac{{\mu }_o(N^{\prime }{)}^2{A}^{\prime }}{l^{\prime }}=\frac{{\mu }_o(2N{)}^{2}A}{2l}$

$⟹$ $L^{\prime }=2\frac{{\mu }_o{N}^{2}A}{l}=2L$