Question

what is an electric dipole?find expression for the torque acting on an electric dipole placed in an external uniform electric field.

Answer 1

Solution :

The force on charge +q

FA−→=qE→FA→=qE→ along the direction of E→E→

The force on charge −q−q

FB−→=qE→FB→=qE→ opposite to the direction of E→E→

As these two forces are equal , unlike and parallel so they forma couple

AC is drawn perpendicular distance between the forces = arm of couple =AC

therefore , torque acting

T=Force×ArmofcoupleT=Force×Armofcouple

=> τ=F×ABsinθτ=F×ABsin⁡θ

=> τ=qE×2asinθτ=qE×2asin⁡θ

=> τ=(q×2a)Esinθτ=(q×2a)Esin⁡θ

=> τ=PEsinθτ=PEsin⁡θ

=> τ=p→×E→