The magnetic field at the center of a current carrying loop of radius 0.1 m is `5sqrt( 5)` times that at a point along its axis. The distance of this point from the centre of the loop is

Options

A. 0.2 m
B. 0.1 m
C. 0.05 m
D. 0.25 m

Answer

A

Explanation

We know that,
`(B_("centre"))/(B_("axis"))=(1+(x^(2))/(r2))^(3//2)`
Given that, `B_("centre")=5sqrt(5)B_("axis")`
`(B_("centre"))/(B_("axis"))=5sqrt(5)`
`therefore 5sqrt(5)=[1+(x^(2))/((0.1)^(2))]^(3//2)`
On squaring both sides, we get
`25xx5 = [1+(x^(2))/((0.1)^(2))]`
`root(3)(125)=1+(x^(2))/((0.1)^(2))`
`rArr 0.01 + x^(2)=0.05`
`rArr x^(2)=0.005 - 0.01`
`rArr x^(2)=0.04`
`rArr x = 0.2 m`