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A small dipole of electric dipole moment $p \hat{j}$ is located on $x$ axis at a distance of $x$ from the origin. A thin infinitely long rod of linear charge density $λ$ is kept along $z$ axis. The force acting on the dipole is

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$\frac{- ρ λ}{2 π \in_{0} x^{2}} \hat{j}$

$\frac{- ρ λ \hat{j}}{2 π \in_{0} x^{3}}$

$\frac{ρ λ}{2 π \in_{0} x^{2}} \hat{j}$

$\frac{ρ λ}{2 π \in_{0} x^{3}} \hat{j}$

answer is C.

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Detailed Solution

$F = ρ \frac{d E}{d x} = \frac{ρ λ}{2 π \in_{0} x^{2}}$ along the dipole

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