What is Electric Potential Energy?
- Just how masses in a gravitational field have gravitational potential energy, charges in an electric field have electric potential energy.
- The electric potential energy, Eₚ, is the amount of work done to assemble a system from infinite separation to a point.
- The total electric potential energy of a system is defined as the work done when brining all the charges of a system to their present positions, assuming they were originally at infinity.
- The electric potential energy for a system of two charged bodies is given by:
- Electric potential is inversely proportional to the separation, r, as both Coulomb's constant and the electric charges remain constant in a system.
- Unlike gravitational potential energy, electric potential energy can be either positive or negative.
- If the two charges have the same signs, then they do work themselves in pushing themselves to infinity separation, as they repel each other.
- Thus electric potential energy is positive.
- If the two charges have opposite signs, then they pull themselves together, and work needs to be done to push them apart to infinite separation.
- The electric potential is thus negative.
- Just like how gravitational force is the derivative of gravitational potential energy, the derivative of electric potential energy is electric potential energy.
- The formula for electric potential has the same arrangement as the one for gravitational potential energy.
- Except the gravitational constant is replaced with Coulomb's constant and mass is replaced with charge.
Sources
https://www.slideserve.com/nuwa/chapter-23-electric-potential