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An electric dipole of dipole moment p is located at a radial distance r (with r >> a, where a is the dipole length) from an infinite line of charge of linear charge density +lambda. The dipole moment vector points along the radial direction r (away from the line). Find the force experienced by the dipole.

1. lambda*p / (2*pi*epsilon0*r²), attractive
2. lambda*p / (2*pi*epsilon0*r³), attractive
3. lambda*p / (2*pi*epsilon0*r²), repulsive
4. lambda*p / (2*pi*epsilon0*r³), repulsive

Correct answer: lambda*p / (2*pi*epsilon0*r²), attractive

Solution

The field of an infinite line charge is E = lambda/(2*pi*epsilon0*r), pointing radially outward, and it decreases with r. A dipole aligned along r sits in this non-uniform field; the force is F = p*(dE/dr) = p * d/dr[lambda/(2*pi*epsilon0*r)] = -p*lambda/(2*pi*epsilon0*r²). The magnitude is lambda*p/(2*pi*epsilon0*r²). With p pointing away from the line, the negative-charge end of the dipole sits in a stronger field (closer to the line) so the net force pulls the dipole toward the line => attractive.

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