The magnetic field at a point due to a magnetic dipole is perpendicular to the magnetic axis. Find the angle that the line joining the point with the centre of the dipole makes with the magnetic axis.

Step-by-step solution

Let the magnetic moment of the dipole be M and the position vector of the point be r . The magnetic field at a point due to a magnetic dipole is given by: B = ₀ 4 r^3 [3( M r ) r - M ] Let the magnetic axis be along the x-axis, so M = M i . The unit vector along the position vector is r = i + j , where is the angle between r and M . Substituting these into the expression for B : B = ₀ M 4 r^3 [3 ( i + j ) - i ] B = ₀ M 4 r^3 [(3 ^2 - 1) i + (3 ) j ] It is given that the magnetic field is perpendicular to the magnet