Potential Energy in External Field — Definition
Definition
Imagine you have a tiny charged particle, like a single electron or a proton. If you place this particle in a region where there's already an electric field – let's call this an 'external field' because it's created by other charges, not the one you just placed – this particle will experience a force.
Just like a ball held above the ground has gravitational potential energy because the Earth's gravitational field exerts a force on it, our charged particle in an electric field also possesses 'electric potential energy'.
Think about it this way: to move the ball higher against gravity, you have to do work. This work gets stored as gravitational potential energy. Similarly, to move a charged particle against the electric force exerted by the external field, you, as an external agent, have to do work. This work isn't lost; it's stored within the system as electric potential energy. If you release the particle, this stored energy can be converted into kinetic energy, causing the particle to move.
The 'external field' is key here. It means we are not considering the field created by the charge we are moving, but rather a pre-existing field. For instance, if you have a large charged plate, it creates an electric field.
When you bring a small test charge near this plate, the test charge gains potential energy because it's interacting with the field of the plate. The amount of potential energy depends on the magnitude of the charge, the strength of the external electric field, and the position of the charge within that field.
For a single point charge at a point where the electric potential due to the external field is , the potential energy is simply . If you have a system of multiple charges, the total potential energy is the sum of the potential energy of each charge in the external field, plus the potential energy of interaction between the charges themselves.
For an electric dipole, which consists of two equal and opposite charges separated by a small distance, its potential energy in an external field depends on its orientation relative to the field. The dipole tries to align itself with the field to reach a state of minimum potential energy, much like a compass needle aligns with the Earth's magnetic field.
Understanding this concept is fundamental to analyzing how charges and dipoles behave in various electrical environments.