A compass needle placed at a distance r from a short magnet in tan A position showns a deflection of `60^(@)`. If the distance is increased to `r(3)^(1//3)`, then the deflection of the compass needle is:

Options

A. `30^(@)`
B. `60^(@)xx(3)^(1//3)`
C. `60^(@)xx(3)^(2//3)`
D. `60^(@)xx(3)^(3//3)`

Answer

A

Explanation

We know that for `tan A` position
`mu_(0)/(4pi)(2M)/r^(3)=H tan theta`
`:. Tan theta prop 1/r^(3)implies(tantheta_(2))/(tantheta_(1))=(r/(r(3)^(1/3)))^(3)=1/3`
`:. tantheta_(2)=(tantheta_(1))/3=(tan 60^(@))/3=sqrt(3)/3=1/sqrt(3)`