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An infinitesimal bar magnet of dipole moment M is pointing and moving with speed v in the +x-direction. A closed small circular conducting loop of radius a and negligible self-inductance lies in the y-z plane with its centre at x = 0 and its axis coinciding with x-axis. Find the force opposing the motion of the magnet, if the resistance of the loop is R. [Assume that x >> a ]

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Force opposing the motion is $\frac{μ_{0}^{2} M^{2} a^{4} v}{R x^{8}}$

force opposing the motion is $F = \frac{9 μ_{0}^{2} M^{2} a^{4} v}{4 R x^{8}}$

force supporting the motion is $\frac{μ_{0}^{2} M^{2} a^{4} v}{R x^{8}}$

No force support or oppose the motion

answer is A.

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Detailed Solution

$B = \frac{μ_{0}}{4 π} \frac{2 M}{x^{3}} \begin{array}{l} ϕ = \vec{B} . \vec{S} \\ e = \frac{- d ϕ}{d t} \\ I = \frac{e}{R} \\ M^{1} = I S \\ F = \frac{μ_{0}}{4 π} \frac{6 M M^{1}}{x^{4}} \end{array}$

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