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Question:

An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper. The radius of the loop is a and distance of its centre from the wire is d (>>a). If the loop applies a force F on the wire then :

F∝(ad)

F∝(a²d³)

F∝(ad)²

F=0

Solution:

Equivalent dipole of given loop
F = m⋅dB/dr
Now, dB/dx = d/dx(μ₀I/2πx) ∝ 1/x²
So F ∝ M/x² [∵ M = NIA]
F ∝ a²/d²