Question

# 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 $$d (>>a)$$. If the loop applies a force $$F$$ on the wire then :

A
F(a2d3)
B
C
D
F=0

Solution

## The correct option is A $$F \propto \left(\dfrac{a}{d}\right)^2$$Eqvilent dipole of given loop$$F = m \cdot \dfrac{dB}{dr}$$Now, $$\dfrac{dB}{dx} = \dfrac{d}{dx} \left(\dfrac{\mu_0I}{2\pi x}\right)$$$$\propto \dfrac{1}{x^2}$$$$\Rightarrow$$ So $$F \propto \dfrac{M}{x^2} [\therefore M = NIA]$$ $$F \propto \dfrac{a^2}{d^2}$$Physics

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