Question

1. Derive an expression for torque acting on an electric dipole placed in a uniform external electric field.
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Answer 1

Answer:

Torque(T) = P×E

Explanation:

Consider an electric dipole consists of -q and +q Charges, seperated by a small distance "2a"

W.K.T Dipole moment is (p) = q ×2a

Let the dipole is placed in uniform Electric filed E, making an angle with the direction of E

Now force on -q charge = -qE

force on +q charge is = +qE

These 2 forces equal in magnitude and opposite in direction

So these 2 will form a couple and gives a torque

Torque = either force × Perpendicular Distance

T= qE× 2aSinθ

= (q×2a) ESinθ

T = PE Sinθ or

T = P×E