Two short magnets of equal dipole moments M are fastened perpendicularly at their centres. The magnitude of the magnetic field at a distance d from the centre on the bisector of the right angle is ( ₀= Permeability of free space)

Step-by-step solution

When two short magnets of equal dipole moments M are fastened perpendicularly at their centres. Then their resultant dipole moment is given as aligned M^ & = M₁^2+M₂^2+2 M₁ M₂ & = M^2+M^2+2 M M 90^ aligned M^ =M 2 ...(i) The magnitude of the magnetic field at a distance d from the centre on the bisector i.e at a distance d on the axial position of dipole, B= ₀ 4 2 M^ d^3 = ₀ 4 2 2 M d^3 [from Eq. (i)]