Potential Energy on Dipole in External Field
Consider a dipole with charges +q and -q placed in a uniform electric field as shown in the figure above. The charges are having a distance d and E be the magnitude of an electric field. The force experienced by the charges is given as –qE and +qE, as can be seen in the figure.
As we know that, when a dipole is placed in a uniform electric field, both the charges completely not experience any force, but it experiences a torque equal to t which is given as
Torque = p⨯E
This torque turn the dipole that is placed parallel /anti-parallel to the field. If we apply an external and opposite torque, it neutralizes the effect of this torque given by external torque and it rotates the dipole from the angle θ0 to an angle θ1 at an very small angular speed without any angular acceleration.
The amount of work done by the external torque is given below:
[Tex]W =\int_{\theta _{0}}^{\theta _{1}}\tau_{ext}(\theta)d\theta = \int_{\theta _{0}}^{\theta _{1}}pESin(\theta)d\theta[/Tex]
W = pE(cos θ0 – cos θ1)
As we know that the work done in bringing a system of charges from infinity to the given configuration is defined as the potential energy of the system, hence the potential energy U(θ) can be associated with the inclination θ of the dipole using the above relation.
Therefore, U(θ) = pE(cos θ0-cos θ1)
In case the dipole moves by 90°, the potential energy is given as
U(θ) = pE (cos π/2 – cos θ) = -pE cos θ = -p.E
Dipole in a Uniform External FieldDipole in a Uniform External Field
If a dipole is in a uniform electric field, it will experience some force and a rotating effect. This rotating effect is known as ‘torque’. Torque is a vector quantity, and its direction generally depends only on the force applied. The torque is calculated based on the rotational effect experienced by the electric dipole as a result of its interaction with the electric field. It arises from the alignment of the dipole moment, which is a vector pointing from the negative to the positive charge, with the direction of the electric field.
In this article we will learn about the topic dipole in a uniform external field but first revise the basic terms like “Torque”, “Dipole”, “electric field”, and dipole in a uniform external field study material.