Question

A bar magnet has a length of 8 cm. The magnetic field at a point at a distance 3 cm from the centre in the broadside-on position is found to be `4 xx 10^-6  "T"`.Find the pole strength of the magnet.

Answer 1

Given:
Length of the magnet, 2l = 8 cm = `8 xx 10^-2 "m"`

Distance of the observation point from the centre of the dipole, d = 3 cm

Magnetic field in the broadside-on position, B = `4 xx 10^-6 "T"`

The magnetic field due to the dipole on the equatorial point (B) is given by 

`B = (u_0m2l)/(4pi(d^2 + l^2)^(3/2)`

Here, m is the pole strength of the magnet.
On substituting the respective values, we get

`4 xx 10^-6 = (10^-7"m" xx 8 xx 10^-2)/(9 xx 10^-4 + 16 xx 10^-4)^(3/2)`

⇒ `4 xx 10^-6 = ("m" xx 8 xx 10^-9)/((25)^(3/2) xx (10^-4)^(3/2)`

⇒ `"m" = (4 xx 10^-6 xx 125 xx 10^-6)/(8 xx 10^-9)`

⇒ `"m" = 6.25 xx 10^-2 "A-m"`