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Question:

The mid points of two small magnetic dipoles of length d in end-on positions, are separated by a distance x, (x>>d). The force between them is proportional to x⁻ⁿ where n is:

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Solution:

Magnetic field due to dipole, B∝1/x³
The interaction energy of two dipole is U = -m⋅B, U∝x⁻³
The force between them, F = -dU/dx, F∝x⁻⁴