Question

Derive an expression for of the torque experienced by an electric dipole in a uniform electric field. What is net force acting on this dipole? ​

Answer 1

Answer:

Torque on Dipole placed in uniform electric field !

First of all we will discuss the force on a electric Dipole placed in uniform electric field :-

Suppose an electric dipole of Dipole moment

|p| = 2aq is placed in a uniform electric field E at an angle ϴ. A force F₁ = qE will act on positive charge and F₂ = -qE on negative charge .

Since, F₁ and F₂ are equal in magnitude but opposite in direction.

Hence , F₁+F₂ = 0 or F net = 0

Thus net force on a dipole in uniform electric field is zero . while in non-uniform electric field it may or may not be zero.

Now let's see what's the torque on the Dipole placed in uniform electric field ....

Torque of F₁ about O is  τ₁ = OA×F₁ = q(OA×E)

Torque of F₂ about O is τ₂ = OB×F₂ = -q(OB×E)

= q(BO×E)

The net torque acting on the Dipole is

τ = τ₁ + τ₂ = q(OA×E) + q(BO×E)

= q(OA+BO)×E

= q(BA×E)

or τ = p×E

or τ = pEsinϴ

where ϴ is the angle between p and E

Explanation:

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