Dipole in a uniform external field

When subjected to an electrical field, positive and negative charges come in many forms, each of which exhibits a distinct set of characteristics.

Have you ever heard the word “electric dipole” used in a sentence? The distribution of positive and negative electric charges in this structure is unexpected, yielding an intriguing physics theory. In more technical terms, an electric dipole is the separation of positive and negative charges.

Consider a pair of opposite signs but equal magnitudes of electric charges separated by a much smaller distance than the distance between the charges themselves. This article will look at how an electric dipole reacts to an external field. We’ll decode and analyse this data in the sections that follow.

If a dipole is maintained in an external electric field, spinning phenomena may occur. External electric field means the electric field that is not generated by the dipole. The rotating force acting on the dipole is the dipole’s torque. This may be performed by calculating the dipole’s net torque generated by its opposing charges.

Dipole in a uniform external field

Given our present knowledge of the effects of an external electric field on charges, we can anticipate a dipole to experience some type of force when exposed to one. A dipole shows remarkable circling behaviour in the presence of an external electric field—the dipole senses ‘torque’ as a consequence of this spinning activity. Calculating the net torque on opposing charges in a dipole to predict total spin is a fascinating issue.

Dipole in a uniform external field derivation

Torque and torque calculation

To compute the torque experienced by a dipole in an external field, we must assume a dipole in a uniform external field. When a positive charge experiences an electric force of size qE in the upward direction, a negative charge experiences a magnitude qE in the downward direction.

The net force is zero indicates that the dipole is in translational equilibrium, as shown by the zero net force. Under some circumstances, the dipole may stay stable while spinning at a constant angular velocity.

This has been shown experimentally, suggesting that both electrostatic forces (qE) operate clockwise. However, the dipole spins when placed in a homogeneous external electric field.

Always remember that torque, regardless of the situation, works in couples. Furthermore, its magnitude is equal to the total of the forces acting on it plus the length of the arm. The arm of a dipole may be thought of as the distance between the point of force application and the point of rotation.

Torque

The force that causes an item to rotate around an axis is known as torque. The axis force dictates the direction of torque, which is a vector quantity. The torque vector’s magnitude is computed as follows:

τ = F r sinθ

where,

F is the force acting on the axis, r is the length of the moment arm, θ is the angle between the force vector and moment arm and τ is the torque vector.

Electric dipole

An electric dipole is a pair of equal and opposing electric charges separated by d. The electric dipole moment is the product of the magnitude of these charges and the distance between them. The electric dipole moment is a vector having a negative to positive charge orientation.

The electric dipole moment, 

p = q d

where

q is the magnitude of the charge, d is the separating distance

Dipole in a uniform external field derivation: The torque equation 

Let us consider a dipole consisting of two positive and negative charges, respectively, that form a dipole since a distance of d separates them. Place it in a homogeneous electric field of strength E, with the dipole’s axis creating an angle of the electric field, and see how it behaves.

The negative sign shows that torque is in the clockwise direction.

The force on the charges, F = ± q E

The components of the force perpendicular to the dipole, F = ± q E sinθ

Since these components are equal and are separated by a distance d, the torque on the dipole is:

Torque = Force × distance between forces

τ = (q E sinθ) d = q d E sinθ

Because ‘qd’ is the magnitude of the dipole moment (p), and the direction of the dipole moment (p) is from positive to negative charge, torque is the cross product of the dipole moment and the electric field (E). If the electric field has a positive polarity, then the torque will rotate in a clockwise direction (therefore negative).

Thus,

τ = – p E sinθ

Observations on net force and torque

The following observations will be made on the nature of the electric field and the location of the dipole:

• If the dipole and external electric field are parallel, their angle is equal to zero; the dipole will feel no torque from the electric field.
• If the external electric field is not uniform, the net force on the dipole may not be zero, but torque will continue to act on it.
• When the dipole’s exterior and internal electric fields are anti-parallel, that is, when the angle between them is higher than zero, the dipole experiences no torque.
• Because the electric dipole and electric field have a parallel connection, the direction of the net force will be in the direction of the growing electric field.
• The dipole’s orientation governs the direction of the net force.
• Because the electric dipole and electric field are anti-parallel, the direction of the net force will be in the direction of the decreased electric field.
• The orientation of a dipole in free space affects the force and torque delivered to it by a uniform external field.

Significance

When we comb our dry hair and place it near a pile of paper scraps, the comb seems to attract the paper scraps. When we comb our hair, the comb gathers charge as we rub, and this charge is utilised to induce charge in the uncharged paper. Alternatively, the comb polarises the pieces of paper, generating a net dipole moment in the direction of the electric field. Due to the non-uniformity of the electric field, the paper fragments gravitate toward the comb direction.

Conclusion

In this article, we talked about dipole in a uniform external field as well as its derivation. Because of the non-uniformity of the external electric field, when the dipole is put in it, the charges +q and q of the dipole do not experience equal and opposing forces. As a result, there is a net force acting on the dipole, the magnitude of which is dependent on the angle formed by the dipole moment concerning the external electric field. Torque is the unit of measure for the amount of force required to induce an item to spin around an axis.