Torque on Dipole

The term dipole in science is indeed a very mysterious word and doesn’t stop to surprise us as and when different topics are discussed. We are already familiar with the fact that the charge exists around us and along with its existence, its presence leads to several natural phenomena as well. In addition, we can say that the positive and negative charges are present in different forms that showcase diverse properties in the attendance of a motivating field.

Have you ever heard about the concept of an electric dipole or dipole? This unique setup of electric charges, i.e. the positive and negative charges, does form an interesting concept of physics. In this article, we are going to discuss the topic of dipole and torque. To be precise, the electric dipole can be tagged as a separation between positive and negative charges.

Electric Dipole

The term dipoles whether they are electric or magnetic can be characterized by their dipole moment which is a vector quantity. For the simple electric dipole, we can say that the electric dipole moment points from the negative charge towards the positive charge and have a magnitude that is equal to the strength of each charge times the separation between the charges. 

To be precise, we can understand it as for the definition of the dipole moment one should always consider the "dipole limit" where for example there is the distance of the generating charges that should converge to 0. 

The moment of an electric dipole is a measure of the separation of positive and negative electrical charges within a system. That is said to be the measure of the system's overall polarity. The SI units for the moment of the electric dipole are coulomb-meter (C⋅m). However, a very commonly used unit in atomic physics and chemistry is the debye denoted as D.

The value obtained from the magnitude and the distance between the charges is the moment of the electric dipole. The moment of an electric dipole is a vector with a clear direction from bad to good charging.

Electrical dipole moment is given by,

p = qd

Where,

q is magnitude

d dividing distance

Theoretically, we can say that an electric dipole is defined by the first-order term of the multipole expansion; it consists of two opposite and equal charges that are infinitesimally close together. Although the dipoles really have separated charges. 

However, we will notice that when making measurements at a distance that is much larger than the charge separation then the dipole gives a good approximation of the actual electric field. The dipole is generally represented by a vector which is from the negative charge towards the charge that is positive.

We often notice in subjects like physics the dimensions of a massive object can be ignored and can be treated as a pointlike object that is of a point particle. 

Torque on Electric Dipole Explanation

Consider a dipole located in the same position ‘E’ to calculate the torque received by the dipole when positioned outside. The compulsory charge will be placed below the ‘qE’ magnitude as you go up, while the negative charge will be placed below the ‘qE’ magnitude as you go down.

Since the absolute power is zero, it can be seen that the dipole is in the equation at the moment. But what is the rotation rate? In this case, the dipole may remain stable but rotates at a certain angular velocity. This fact has been demonstrated by experimentation, and it shows that both electrostatic forces (qE) act as clock-related torque. 

As a result, when a dipole is inserted into the same external electrical circuit, it rotates. Torque always works with external force applied which will be in pairs. Moreover, its size is a result of its strength and arm. The arm can be thought of as the distance between the point of force applied and the point at which rotation occurs at the dipole.

Torque

Torque (τ) = Force × distance separating forces

Torque is a vector whose direction is determined by the force acting on the axis. The magnitude of the torque vector is determined as follows:

T = F r sinθ

Which means,

F - force acting on the axis

r - temporary arm length

θ - angle between force vector and temporary arm

τ - is the vector of torque

Derivation of Torque 

Consider a dipole with the angles of + q and q forming a dipole because they are separated by a distance of d. Positioned in the same electric field of power E, the dipole axis forms an θ angle with an electric field.

Charging power, F = ± q E 

Elements of power perpendicular to dipole, F = ± q E sinθ

Since ‘qd’ is the magnitude of the dipole moment (p), and the direction of the dipole moment ranges from positive to negative; torque is the product of a dipole moment cross and an electric field. When the direction of the electric field is positive, the torque is in the clock (therefore negative) in the image above.

So,

τ = - pE sinθ

An incorrect sign indicates that the torque is in the clockwise direction.

Torque on a Dipole in a Uniform Electric Field

Now, we consider a dipole with charges that is +q and –q which is forming a dipole since they are a distance d away from each other. Now let it be placed in a uniform electric field which is of strength denoted as E such that the axis of the dipole forms an angle θ with the electric field.

An electric dipole in an electric field that is external is subjected to a torque written as τ = pE sin θ 

Where symbol θ is the angle which is between p and E. The torque tends to align the moment of the dipole p in the direction of E. 

The potential energy which is of the dipole is given by 

Ue = −pE cos θ 

or in the vector notation that is, 

Ue = −p · E 

Conclusion

• The force that causes an object to rotate on an axis is known as torque.

• A pair of electric charges of the same size but the opposing charges divided by the ‘d’ range is known as the electric dipole.

• Since the magnitude of the force is equal to and divides by a distance of d, the torque on the dipole is given:Torque(τ) = Power x dividing forces .