A circular current-carrying coil has a radius `R`. The distance from the centre of the coil, on the axis, where `B` will be `1//8` of its value at the centre of the coil is

Options

A. `R//sqrt3`
B. `sqrt3R`
C. `2Rsqrt3`
D. `(2sqrt3)R`

Answer

B

Explanation

(b) `B_("axis")=(mu_0)/(4pi)xx(2pilR^2)/((R^2+x^2)^(3//2))`
At centre, `B_(centre)=(mu_0)/(4pi)xx(2pil)/R`
In the given problem,
`(mu_0)/(4pi)xx(2pilR^2)/((R^2+x^2)^(3//2))=1/8[(mu_0)/(4pi)xx(2pil)/R]`
or `(R^2+x^2)^(3//2)=8R^2`
Solving, we get `x=Rsqrt3`