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A tiny electric dipole ( $H_{2} O$ molecule) of dipole moment $\vec{p}$ is placed at a distance r form an infinitely long wire, with its normal to the wire in the same plane. If the linear charge density of the wire is $λ$ , the electrostatic force acting on the dipole is equal to

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$\frac{λ P}{2 π ε_{0} r^{2}}$

$\frac{λ P}{π ε_{0} r}$

$\frac{2 λ P}{π ε_{0} r}$

$\frac{λ P}{4 π ε_{0} r}$

answer is D.

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Detailed Solution

$F = \frac{- \partial v}{\partial r} = \frac{- \partial}{\partial r} (\frac{p λ}{2 π ε_{0} r}) = \frac{p λ}{2 π ε_{0} r^{2}}$

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