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

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Solution:

Eqvilent dipole of given loop
$F =m . \frac{dB}{dr} $
Now $ \frac{dB}{dx} = \frac{d}{dx} \left(\frac{\mu_{0}I}{2\pi x}\right) $
$ \propto\frac{1}{x^{2}} $
$ \Rightarrow \text{So} F \propto \frac{M}{x^{2}} \left[\because M = NIA\right] $
$ \therefore F \propto\frac{a^{2}}{d^{2}} $

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