Question

obtain the expression for torque acting on a dipole in 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

Explanation:

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Answer 2

Let us assume an electric dipole is placed in a uniform magnetic field as shown in figure. Each charge of dipole experience a force qE in electric field. Since points of action of these forces are different, these equal and anti paralel forces give rise to a couple that rotate the dipole and make the dipole to align in the direction of field.

The torque τ experienced by the dipole is (qE)×(2dsinθ), where 2d is the length of dipole and θ is the angle between dipole and field direction.

begin mathsize 12px style tau space equals space q E cross times 2 d sin theta space equals space open parentheses q cross times 2 d close parentheses cross times E space sin theta space equals space p cross times E space sin theta space equals space bold italic p bold space bold cross times bold space bold italic E end style

we have used the definition of dipole moment p = q×2d in the above equation. p and E are vectors representing the dipole moment and Electric field respectively.

Last step shown above is the cross product of two v