Question

Magnetic fields at two points on the axis of a circular coil at a distance of `0.05m` and `0.2 m` from the centre are in the ratio `8:1`. The radius of the coil is
A. `1.0 m`
B. `0.1 m`
C. `0.15 m`
D. `0.2 m`

Answer 1

Correct Answer - B
`B=(mu_(0))/(4pi)xx(2piNiR^(2))/((R^(2)+x^(2))^(3//2)) implies B prop (1)/((r^(2)+x^(2))^(3//2))`
`implies (8)/(1)=((R^(2)+x_(2)^(2))^(3//2))/((R^(2)+x_(1)^(2))^(3//2)) implies ((8)/(1))^(3//2)=(R^(2)+0.04)/(R^(2)+0.0025)`
`implies (4)/(1)=(R^(2)+0.04)/(R^(2)+0.0025)`. On solving `R=0.1 m`