The needle of a deflection galvanometer shows a deflection of `60^(@)` due to a short bar magnet at a certain distance in tan A position. If the distance is doubled, the deflection is

Options

A. `sin^(-1)(sqrt(3)/8)`
B. `cos^(-1)(sqrt(3)/8)`
C. `tan^(-1)(sqrt(3)/8)`
D. `cot^(-1)(sqrt(3)/8)`

Answer

C

Explanation

For short bar magnet in tan A-position
`mu_(0)/(4pi)(2M)/d^(3)=H tantheta …(i)`
When distance is double, then new deflection `theta^(')` is given by
`mu_(0)/(4pi)(2M)/((2d)^(3))=H tantheta^(') …(ii)`
`:. (tantheta^('))/(tantheta^('))=1/8impliestantheta^(')=(tantheta)/8=(tan60^(@))/8=sqrt(3)/8`
`impliestheta^(')=tan^(-1)(sqrt(3)/8)`