Magnetic induction at a point P on the axis is 54 times the magnetic induction at a point Q on the equator of a short magnetic dipole. The ratio of the distances of the points P and Q from the dipole is given by

Options

A. `r_(P)/r_(Q)=3`
B. `r_(P)/r_(Q)=1/2`
C. `r_(P)/r_(Q)=2/1`
D. `r_(P)/r_(Q)=1/3`

Answer

D

Explanation

Given : `B_("axis")=54 (B_("equator"))`
`mu_(0)/(4pi)(2M)/r_(P)^(3)=54 [mu_(0)/(4pi)xxM/r_(Q)^(3)]`
`:. 1/r_(P)^(3)=27/r_(Q)^(3)`
Taking the cube roots of both sides, we get
`:. 1/r_(P)=3/r_(Q)" ":. 3 r_(P)=r_(Q)" ":. r_(P)/r_(Q)=1/3`