Question

If length of a solenoid is increased then what change should be made on no. of turns to keep self inductance constant-

• A. increase
• B. remain same
• C. decrease
• D. none of these

Answer 1

The correct option is A increase

$N$=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= $E=NBA$

$⟹E=N\times {\mu }_o\frac{N}{l}i\times \pi R^2$

$⟹E=\frac{{\mu }_o{N}^2\pi R^2}{l}i=Li$

where $L$=self inductance

Thus, $L=\frac{{\mu }_o{N}^2\pi R^2}{l}$

For constant $L$, $N^2\propto l$

Hence, on increasing length of coil, number of turns should be increased to keep $L$ constant.

Answer-(A)