As illustrated in the figure, two short magnets with equal dipole moments M are joined perpendicularly at their centres. What is the magnitude of the magnetic field at a distance d from the centre along the bisector of the right angle?

Step-by-step solution

Let the centre of the two magnets be at the origin (0,0) . The horizontal magnet has its South pole on the left and North pole on the right. Its magnetic dipole moment is directed from South to North, so M ₁ = M i . The vertical magnet has its South pole at the bottom and North pole at the top. Its magnetic dipole moment is also directed from South to North, so M ₂ = M j . The net magnetic dipole moment of the system is the vector sum of the individual dipole moments: M _ net = M ₁ + M ₂ = M i + M j The magnitude o