A circular current carrying coil has a radius R. The distance from the centre of the coil on the axis where the magnetic induction will be `(1//8)^(th)` of its value at the centre of the coil is,

Options

A. `R/(sqrt(3))`
B. `Rsqrt(3)`
C. `2sqrt(3) R`
D. `2/(sqrt(3)) R`

Answer

B

Explanation

`(B_("centre"))/(B_("axis"))=(1+(x^(2))/(R^(2)))^(3//2)` , also `B_("axis")=(1)/(8)B_("centre")`
`= gt 8/1 B_("centre")`
`implies 8/1 =(1+(x^(2))/(R^(2)))^(3//2) implies 2=(1+(x^(2))/(R^(2)))^(1//2)`
`implies 4=1+(x^(2))/(R^(2)) implies 3=(x^(2))/(R^(2))= 3R^(2) implies x=sqrt(3)R`