A short magnet produces a deflection of `37^@` in a deflection magnetometer in `Tan-A` position when placed at a separation of 10cm from the needle. Find the ration of the magnetic moment of the magnet to the earth's horizontal magentic field.

Explanation

Given `theta = 37^(@)`
`d = 10 cm = 0.1m`
`We know that
`(M)/(B_(H)) = (4 pi)/(mu_(0)) ((d^(2) - l^(2))/(2d) tan theta`
[as the magnet is short]
`= (4 pi)/(mu_(0)) xx (d^(4))/(2d) tan theta`
` = (4 pi)/(4 pixx 10^(-7)) xx ((90.1)^(2))/(1) xx tan 37^(@) `
`= 0.5 xx 0.75 xx 1 xx 10^(-2) xx 10^(-7)`
`= 0.5 xx 0.75 xx 1 xx 10^(-3) xx 10^(-7)`
`= 0.357 xx 10^(4) `
` = 0.75 xx 10^(2) A - m^(2)//T`