Question

A deflection magnetometer is placed with its arms in north-south direction. How and where should a short magnet having M/B_H = 40 A m² T⁻¹ be placed so that the needle can stay in any position?

Answer 1

Given : 

Ratio , `M/B_H = 40 "Am"^2"/"T`

Since the magnet is short, l can be neglected.

So, using the formula for `M/B_H` from the magnetometer theory and substituting all values, we get 

`M/B_H = (4pi)/(u_0) (d^3)/2 = 40`

⇒ `d^3 = 40 xx 10^-7 xx 2`

⇒ `d^3 = 8 xx 10^-6`

⇒ `d = 2 xx 10^-2  "m" = 2  "cm"`

Thus, the magnet should be placed in such a way that its north pole points towards the south and it is 2 cm away from the needle.