Question

Self-Inductance of a Long Solenoid is proportional to(where $r$ is radius of solenoid)-

• A. $r$
• B. $r^2$
• C. $r^3$
• D. does not depend upon $r$

Answer 1

The correct option is B $r^2$

$N$=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= $E=NBA$

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

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

where $L$=self inductance

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

Hence, $L\propto R^2$

Answer-(B)