Question

Area of a long solenoid is doubled.So how many times we have to increase its length to keep its self inductance constant-

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

$N$=total number of turns in solenoid

$l$=length of solenoid

$R$=radius of cross section of solenoid

Magnetic field inside solenoid =$B={\mu }_o\frac{N}{l}i$ where, $\frac{N}{l}$=number of turns per unit length

Now, emf induced= $E=NBA$

$⟹E=N\times {\mu }_o\frac{N}{l}i\times A$

$⟹E=\frac{{\mu }_o{N}^{2}A}{l}i=Li$

where $L$=self inductance

$⟹L=\frac{{\mu }_o{N}^{2}A}{l}$

$⟹L\propto \frac{A}{l}$

The length of solenoid should be doubled also on doubling the area to keep $L$ constant.

Answer-(B)