If the magnitude of the intensity of a magnetic field at a distance x on the axial line and at a distance y on the equatorial line of a given dipole have the same value the Ratio x:y is

Options

A. `1:sqrt2`
B. `sqrt2:1`
C. `1:2`
D. `2^(1/3):1`

Answer

D

Explanation

Magnetic field at a distance x on axial line, `B_(1)=(mu_(0))/(4pi)(2M)/(x^(3))`
On equatorial line, `B_(2)=(mu_(0))/(4pi)(M)/(y^(3))`
Given `B_(1)=B_(2)`
`(mu_(0))/(4pi)(2M)/(x^(3))=(mu_(0))/(4pi)(M)/(y^(3))`
`implies (x^(3))/(y^(3))=2/1`
`therefore x:y=2^(1/3):1`