Torque on a Dipole in a Uniform Electric Field

Understanding Torque on a Dipole in a Uniform Electric Field

An electric dipole is created when there is a separation of positive and negative charges. 

Before we can comprehend the effects of the torque operating on an electric dipole in a uniform electric field, we must first understand the properties of the torque acting on an electric dipole in a uniform electric field. First and foremost, let us review our grasp of torque and electric dipole. 

Torque

Torque is a vector quantity whose direction and force’s direction on the axis usually determine its direction. The torque vector’s magnitude is stated to be determined in the following way:

As: τ = FrsinΘ

The letter r denotes the moment arm’s length, and the Θ expresses the angle between the force vector and the moment arm.

Torque on Electric Dipole

Dipoles are pretty much the same thing as charge separation. Unlike other vectors, the moment of an electric dipole has a specific direction, namely from negatively charged to positively charged.

That is given as p=qd

When there is a homogeneous electric field, the torque on an electric dipole is zero.

Now assume a dipole that has the charges: +q and –q that form a dipole because a distance of d separates them. In this case, the dipole should be positioned in the electric field that is uniform in nature and has sufficient strength, represented by E, here the dipole’s axis generates an angle θ with the electric field.

An electric dipole in a uniform external field experiences a torque given as τ = pE sin θ, where the symbol θ denotes the angle between p and E. The moment of the dipole p tends to align in the direction of E as a result of the torque. 

The potential energy of the dipole Ue = −pE cos θ or in the vector notation that is Ue = –pE. 

What is the Torque on Dipole in an Uniform Electric Field?

For example, take a dipole having the charges +q and –q; both create a dipole as they have a distance between them indicated by d. Allow it to be immersed in an electric field that is uniform in nature with E strength, in such a way that the dipole’s axis makes a right angle with respect to that electric field.

Torque is the unit of force that causes an object to spin around an axis completely.

An electric dipole refers to an electric pair of charges having similar magnitudes but opposite in nature and maintaining a distance ‘d’ from one another. Because the charges experiences two identical force of equal magnitude, the dipole’s torque may be calculated as follows:

Torque (τ) = Force × distance separating forces

No matter whether the dipoles are electric or magnetic, they can all be distinguished by their dipole moment, which is a vector variable. In the case of a simple electric dipole, we may state that the electric dipole moment tends to point from the – charge towards the + charge and maintains a value of magnitude corresponding to the strength of every charge multiplied by the displacement given between the charges. To be more specific, we may define it as always considering the “dipole limit” while defining the moment of the dipole, where the distance between the producing charges, for example, should converge to 0.

The separation of positive and negative electrical charges inside a system is measured by the moment of an electric dipole. This is supposed to measure the overall polarity of the system. Coulomb-metre (Cm) is the unit of measure for the moment of the electric dipole in the SI system. The debye, abbreviated as D, is a widely used unit in atomic physics and chemistry.

Conclusion 

Here we learned about the torque on a dipole in a uniform electric field. The first-order component of the multipole expansion defines a dipole in a uniform electric field theory; it consists of two opposed and equal charges that are infinitesimally close together. Even though the dipoles have different charges—when measuring at a distance far greater than the charge separation, the dipole provides a decent approximation of the actual electric field. The dipole is usually represented as a vector that runs from the negative charge to the positive charge.