Two short bar magnets A and B are arranged co-axially. The distance between their centres is 30 cm. A compass needle placed on their axis at a distance of 6 cm from B shows no deflection. The ratio of the magnetic moments of A and B is

Options

A. `16:1`
B. `1:16`
C. `64:1`
D. `1:64`

Answer

C

Explanation

Given,
distance between the magnets, d = 30 cm
compass neddle distance from magnet, B = 6 cm
Now, distance of magnet A from needle,
`d_(1)=30-6=24 cm`
and distance of magnet B from needle, `d_(2)=6 cm`
`therefore` Magnetic field on a axial line is given as,
`" "B=(mu_(0))/(4pi)(2M)/(d^(3))`
Hence, the ratio of the magnetic moment for A and B
`" "M_(1)/d_(1)^(3)=M_(2)/d_(2)^(3)`
`" "M_(1)/M_(2)=(d_(1)/d_(2))^(3)`
`therefore " "d_(1)=24 cm, d_(2)=6 cm`
`" "M_(1)/M_(2)=(24/6)^(3)`
`" "M_(1)/M_(2)=(4)^(3)=64`
So, the ratio of the magnetic moments of A and B is 64 : 1.