Question

Derive an expression for the torque acting on an electric dipole placed in an uniform electric field

Answer 1

Answer: Let inside the uniform magnet field the electric dipole is placed. Let the force of qE is applied in the electric field on each charge of the dipole.

A couple rotate the dipole during to the equal and opposite force on the points of action. The torque(T) of the dipole is (qE×2dsinθ where d is the length of the dipole and θ is angle between the dipole and the direction of the field.

T=qE×2dSinθ

=q×2d×Sinθ

=p×ESinθ

T =p×E

Answer 2

Answer:

The expression of torque acting on an electric dipole placed in a uniform electric field is given by

τ = p x E
where, τ is the torque on the electric dipole
            P is the dipole present in the field
            E is the electric field

Explanation:

For the derivation, we need to assume the following

Let,

p be the dipole moment of an electric dipole placed in an electric field

E be the electric field​, making an angle θ with the direction of the field.

Consider 2 charges present in the field, experiencing equal and opposite forces. F and -F​

Their magnitude can be written as $\overarrow F = qE$

These two charges form a dipole because they have different lines of action with equal and opposite forces.

Therefore, the magnitude of the moment of torque is,

$\tau = F\times AC \\\tau = qE(2sin\theta)\\\tau = qEsin\theta$

This gives us the value of torque acting on the dipole, which aligns to the dipole moment parallel to the electric field.

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