Question

Self inductance of long solenoid is directly proportional to-($A$ is area of cross section)

• A. $A$
• B. $A^2$
• C. $A^3$
• D. $A^4$

Answer 1

The correct option is A $A$

$N$=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= $E=NBA$

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

$⟹L\propto A$

Answer-(A)