Question

If area of a long solenoid is doubled,length is trippled and no. of turns are remained contant.Then its self-inductance will be changed how many times-

• A. $1/3$
• B. $2/3$
• C. $1/9$
• D. $4/3$

Answer 1

The correct option is B $2/3$

$N$=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

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

Hence, on doubling area and tripling the length of solenoid,

$L$ becomes $\frac{2}{3}$ times.

Answer-(B)