Question

A simple dipole consists of two charges with the same magnitude, q, but opposite sign separated by a distance d. The EDM (electric dipole moment) of the configuration is represented by p which has a magnitude p = qd and a direction pointing from the negative charge towards the positive charge. If the dipole is located in a region with an electric field, E, then it experiences a torque τ = p × E. In this problem we will explore the rotational potential energy of an electric dipole in an electric field. Enter an expression, in simplified form, for the amount of work, dW, done by the electric field on the dipole when it undergoes a rotation by dθ.

Answer 1

Answer:

a. dW = ∫pEsinθdθ  b. W = p.E

Explanation:

a. We know torque τ = p × E = pEsinθ where θ is the angle between p and E

Let the torque τ rotate the dipole by an amount dθ. So, the workdone dW = ∫τdθ = ∫pEsinθdθ

b. So, the total work done is gotten by integrating from 90 to θ. So,

W = ∫₉₀⁰dW

= ∫₉₀⁰pEsinθdθ

= pE∫₉₀⁰sinθdθ

= pE(cosθ - cos90)

=pEcosθ

= p.E