The ratio of magnetic inductions at the centre of a circular coil of radius a and on its axis at a distance equal to its radius, will be-

Options

A. `1/(sqrt(2))`
B. `(sqrt(2))/1`
C. `1/(2sqrt(2))`
D. `(2sqrt(2))/1`

Answer

D

Explanation

`B_(c)=(mu_(0)i)/(2a)`
`B_(R)=(mu_(0)ia^(2))/(2(a^(2)+a^(2))^(3//2))=(mu_(0)i)/(4sqrt(2)a)`
`(B_(C))/(B_(R))=(2sqrt(2))/1`