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. `sqrr 3R`
B. `(R )/(sqrt3)`
C. `((2)/(sqrt3)) R`
D. `(R )/(2 sqrt3)`

Answer

A

Explanation

It is given that `B_("axis") =1/8 (B_("centre"))`
`therefore (mu_(0))/(4pi)[(2pi IR^(2))/((R^(2)+x^(2))^(3//2))]=1/8 xx(mu_(0))/(4pi) ((2pi I)/(R))`
`therefore (mu_(0))/((R^(2)+x^(2))^(3//2))=(1)/(8R)`
`therefore (R^(2) +x^(2))^(3//2)=8 R^(3) =(2 R )^(3)`
`therefore (R^(2)+ x ^(2)) ^(3//2) = [(2 R) ^(3) ]^(2//3) =4 R ^(2)`
`therefore 3 R^(2) =x^(2) thereforex = sqrt3R`