Question

An electric dipole consists of two point charges +1 µC and −1 µC, held 10 cm apart. It is subjected to a uniform electric field of 100 N/C. Calculate the amount of work done in turning the dipole from its position of stable equilibrium to the position of unstable equilibrium, in the field.

Answer 1

Given: Charge (q) = 1 µC = 10⁻⁶ C

Separation (2l) = 10 cm = 0.1 m

Electric field (E) = 100 N/C

Initial angle (θ₁) = 0° (Stable)

Final angle (θ₂) = 180° (Unstable)

First, calculate the dipole moment (p):

p = q × 2l

= 10⁻⁶ C × 0.1 m

= 10⁻⁷ C . m

Now, calculate the work done (W) = pE(cos θ₁ − cos θ₂)

= pE(cos 0° − cos 180°)

= pE(1 − (−1))

= 2pE

= 2 × 10⁻⁷ × 100

= 2 × 10⁻⁵ J

∴ The amount of work done is 2 × 10⁻⁵ J.