Find the pole strength of a magnet of length 2 ~cm , if the magnetic field strength B at distance 10 ~cm from the centre of a magnet on the axial line of the magnet is 10⁻⁴ ~T .

Step-by-step solution

The magnetic field B on the axial line of a short magnet at a distance d from its centre is given by the formula B = ₀ 4 2Md (d^2 - l^2)^2 , where M is the magnetic dipole moment, 2l is the length of the magnet, and d is the distance from the centre. Given 2l = 2 cm = 0.02 m , so l = 0.01 m . The distance d = 10 cm = 0.1 m . The magnetic field B = 10⁻⁴ T . Since d l , we can approximate the formula as B = ₀ 4 2M d^3 . Substituting the values, 10⁻⁴ = 10⁻⁷ 2M (0.1)^3 . 10⁻⁴ = 10⁻⁷ 2M 0.001 = 10⁻⁴ 2M . Therefore, 2M =