Find the distance at which the magnetic field on axis as compared to the magnetic field at the centre of the coil carrying current I and radius R is `1/8`.

Options

A. R
B. `sqrt2R`
C. 2R
D. `sqrt3R`

Answer

D

Explanation

`B_("centre")/B_("axis")=[1+x^(2)/R^(2)]^(3/2),"But "B_("axis")=(B_("centre"))/8`
`thereforeB_("centre")/B_("axis")xx8=[1+x^(2)/R^(2)]^(3/2)`
`therefore(2^(3))^(2/3)=1+x^(2)/R^(2)`
`therefore(2^(2))=[1+x^(2)/R^(2)]`
`therefore4=1+x^(2)/R^(2)" "thereforex^(2)/R^(2)=3rArrx=sqrt3R`