Two identical short bar magnets, each of magnetic moment M, are placed coaxially with their centres separated by distance r, where r is much larger than their lengths. Like poles face each other.
The magnitude of force between the magnets is:

Question

Two identical short bar magnets, each of magnetic moment M, are placed coaxially with their centres separated by distance r, where r is much larger than their lengths. Like poles face each other.

The magnitude of force between the magnets is:

G1 Physics · Accepted Answer

For two coaxial short magnetic dipoles, the interaction-energy magnitude is |U| = (μ₀/4π)·(2M₁M₂/r³). For identical magnets, |U| = μ₀M²/(2πr³). The force magnitude is obtained from F = |-dU/dr|. Hence, F = 3μ₀M²/(2πr⁴). Like poles facing corresponds to repulsion, but the question asks only for magnitude.