Question

A dipole, having dipole moment \(\vec{p}\) is placed in an electric field \(\vec{E}\). What will be the torque acting on the dipole?

(a) \(\vec{p}.\vec{E}\)

(b) \(\vec{p}+\vec{E}\)

(c) \(\vec{p} \times \vec{E}\)

(d) \(\vec{p}-\vec{E}\)

The question was posed to me in exam.

Enquiry is from Dipole in a Uniform External Field in portion Charges and Fields of Physics – Class 12

Answer 1

The correct choice is (c) \(\vec{p} \times \vec{E}\)

To explain: Forces on +q and –q charges act along two opposite direction and the perpendicular distance between the two forces is equal to 2lsinθ (as the distance between the two point charges is 2l). Therefore the torque = force*distance=qE*2lsinθ=(q*2l)*E*sinθ. But q*2l is defined as the dipole moment \(\vec{p}\) of the dipole. So the expression of torque becomes \(\vec{p} \times \vec{E}\) according to cross product rule.