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