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

Options

A. `2:1`
B. `1:2`
C. `1:4`
D. `4:1`

Answer

A

Explanation

Here L, `mu_0, l , pi` are same in the equation of self-inductance of solenoids,
`L=(mu_0N^2A)/l`
`therefore N^2 prop 1/r^2`
`therefore N_2/N_1=r_1/r_2`
`therefore (200/100)=r_1/r_2`
`therefore r_1/r_2=2/1`