A dipole of dipole moment p is placed at a distance r from an infinite line charge with linear charge density lambda. What is the force on the dipole if it is oriented perpendicular to the line charge?

A. p 2 _0 r^2 — The force on a dipole in a non-uniform electric field is given by the gradient of the potential energy or the product of the dipole moment and the field gradient.

JEE Main · PhysicsHard

$A dipole of dipole moment p is placed at a distance r from an infinite line charge with linear charge density λ . What is the force on the dipole if it is oriented perpendicular to the line charge?$

A. $\frac{p λ}{2 π ϵ _{0} r ^{2}}$
B. $\frac{p λ}{π ϵ _{0} r ^{2}}$
C. $\frac{p λ}{4 π ϵ _{0} r ^{2}}$
D. $0$

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Correct answer: A — $\frac{p λ}{2 π ϵ _{0} r ^{2}}$

Solution

$The electric field of an infinite line charge is E = \frac{λ}{2 π ϵ _{0} r} .$
$The force on a dipole is F = p \frac{d E}{d r} .$
$Differentiating the field with respect to r, we get \frac{d E}{d r} = - \frac{λ}{2 π ϵ _{0} r ^{2}} .$
$The magnitude of the force is F = p \frac{λ}{2 π ϵ _{0} r ^{2}} .$
$Hence the answer is (A).$

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A dipole of dipole moment p is placed at a distance r from an infinite line charge with linear charge density λ. What is the force on the dipole if it is oriented perpendicular to the line charge?

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$A dipole of dipole moment p is placed at a distance r from an infinite line charge with linear charge density λ . What is the force on the dipole if it is oriented perpendicular to the line charge?$