Potential Energy of a Dipole in an External Field
Potential Energy of a Dipole in an External Field
Suppose a dipole with charges q1 = +q and q2 = –q is placed in a uniform electric field E. The dipole feels no net force in a homogeneous electric field but does experience a torque defined as,
τ = p × E
which will tend to rotate it.
Assume that an external torque τext is applied in such a way that it simply neutralizes the torque and rotates it in the plane of paper at an infinitesimal angular speed and without angular acceleration from angle θ0 to angle θ1. The amount of work done by the external torque can be written as,
This work is saved as the system’s potential energy. The potential energy U(θ) can then be linked to the dipole’s inclination θ. There is a degree of freedom in choosing the angle at which the potential energy U is regarded to be zero, just as there is with other potential energies. Taking θ0 = π/ 2 is a natural decision.
This expression can alternately be understood also from Equation (3). apply Equation (3) to the present system of two charges +q and –q.
……(4)
The location vectors of +q and –q is denoted by r1 and r2. The work done in transporting a unit positive charge against the field from r2 to r1 is now equal to the potential difference between positions r1 and r2. 2a×cosθ is the displacement parallel to the force.
Therefore, [V(r1) – V(r2)] = -E×2a×cosθ
So, equation (4) can be written as,
Note, U′(θ) differs from U(θ) by a quantity which is just a constant for a given dipole.
Potential Energy in an External Field
When an external force operates to conduct work, such as moving a body from one location to another against a force like spring force or gravitational force, the work is gathered and stored as potential energy in the body. When an external force is removed, the body moves, acquiring kinetic energy and losing potential energy in equal amounts. As a result, the total kinetic and potential energy are conserved. Conservative forces are those who belong to this group. Spring force and gravitational force are two examples of these forces.
Table of Content
- What is Potential Energy?
- Potential Energy in an External Field
- Potential Energy of a Single Charge
- Electric Potential Due to a Point Charge
- Potential Energy of a System of Two Charges in an External Field
- Potential Energy of a Dipole in an External Field
- Electrostatic Potential
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