Question

The self inductance of two solenoids A & B having equal length are same. If the number of turns in two solenoids A & B are $100$ and $200$ respectively. The ratio of radii of their cross-section will be __________.

• A. $2:1$
• B. $1:2$
• C. $1:4$
• D. $4:1$

Answer 1

The correct option is A $2:1$

Self inductance of a solenoids is given by $\frac{{\mu }_0{N}^{2}A}{l}$.

Given. $\frac{{\mu }_0{N}_1^2{A}_1}{l_1}$ = $\frac{{\mu }_0{N}_2^2{A}_2}{l_2}$

$\Rightarrow$ $\frac{100\times 100{\mu }_0{A}_1}{l_1}$ = $\frac{200\times 200{\mu }_0{A}_2}{l_2}$

$\Rightarrow$ $A_1=4A_2(\because l_1=l_2)$

$\Rightarrow$ $\frac{r_1}{r_2}=2$

Therefore, correct answer is $2$.