Two coils are made of same material such that radius of one coil is twice of the other and magnetic field is same at the centres then ratio of potential difference applied across `1^st` to second coil is

Options

A. 2 times
B. same
C. 4 times
D. 3 times

Answer

C

Explanation

For same length
`B=(mu_0 n I)/(2a)`
`I=(B2a)/(mu_0n)` i.e.,`1prop (1)/(a^2)` for same length.
`therefore (I_2)/(I_1)=((a_1)/(a_2))^2`
`(I_2)/(I_1)=((2a_2)/(a_2))^2`
`I_2=4I_1(because Vprop I)`
i.e., `V_2=4V_1`.