How Does Torque Affect an Electric Dipole in a Field?
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 .
FAQs on Torque on Dipole Explained with Examples
1. What is meant by the torque on an electric dipole in a uniform electric field?
The torque on an electric dipole is the rotational force it experiences when placed in an external electric field. When a dipole, which consists of a pair of equal and opposite charges, is placed in a uniform electric field at an angle, the forces on the two charges are equal in magnitude but opposite in direction. These forces form a couple, which does not cause linear motion but produces a turning effect, or torque. This torque tends to align the dipole with the direction of the electric field.
2. What is the formula for the torque acting on an electric dipole in a uniform electric field?
The formula for the torque (τ) on an electric dipole is given by the cross product of the dipole moment (p) and the electric field (E). The vector expression is:
τ = p × E
The magnitude of the torque can be calculated using the formula:
τ = pE sin(θ)
where:
- p is the magnitude of the electric dipole moment.
- E is the magnitude of the uniform electric field.
- θ is the angle between the dipole moment vector and the electric field vector.
3. Under what conditions is the torque on a dipole maximum and minimum?
The torque experienced by an electric dipole depends on its orientation (angle θ) with respect to the electric field.
- Maximum Torque: The torque is maximum when the dipole is placed perpendicular to the electric field. In this case, θ = 90°, and since sin(90°) = 1, the torque is τ_max = pE. This is a position of unstable equilibrium.
- Minimum Torque (Zero): The torque is zero when the dipole is aligned with the electric field. This occurs at two angles: θ = 0° (parallel to the field), which is a state of stable equilibrium, and θ = 180° (anti-parallel to the field), which is a state of unstable equilibrium.
4. Why is the net force on an electric dipole zero in a uniform electric field, but it still experiences a torque?
In a uniform electric field, the field strength is the same at every point. The positive charge (+q) of the dipole experiences a force F+ = qE in the direction of the field, while the negative charge (-q) experiences an equal and opposite force F- = -qE. Since these two forces are equal in magnitude and opposite in direction, the net force on the dipole is zero (F_net = F+ + F- = 0). However, because these forces act at different points, they form a couple that creates a rotational effect, or torque, unless the dipole is already aligned with the field.
5. What is the difference in behavior of an electric dipole in a uniform vs. a non-uniform electric field?
The behavior of an electric dipole differs significantly in the two types of fields:
- In a Uniform Electric Field: The dipole experiences zero net force but a non-zero torque (unless aligned with the field). This causes the dipole to undergo purely rotational motion, attempting to align with the field.
- In a Non-Uniform Electric Field: The electric field strength is different at the locations of the two charges. Therefore, the forces on the positive and negative charges are unequal. As a result, the dipole experiences both a net force and a net torque, causing it to undergo both rotational and translational (linear) motion.
6. What is the physical significance of the torque on a dipole, and where is this concept applied?
The physical significance of the torque is that it describes the mechanism by which an external electric field can orient polar molecules. This tendency to align has several important applications. For example, a microwave oven works on this principle. The oven generates an oscillating electric field. The water molecules (which are permanent dipoles) in the food experience a continuous torque, causing them to rotate back and forth rapidly. This forced rotational motion increases the internal energy of the food, which manifests as heat, thereby cooking it.
7. Can an electric dipole ever experience a net force but no net torque in a non-uniform electric field?
Yes, this special case can occur in a non-uniform electric field. A dipole will experience a net force because the field strength differs at its two ends. However, if the dipole moment vector (p) happens to be aligned perfectly parallel or anti-parallel to the direction of the electric field (E) at its location, the forces on both charges will act along the same line. In this specific orientation, they will not form a turning couple, and the net torque will be zero, even while a net force causes the dipole to accelerate linearly.
