24.1 - Electric potential energy
Electric potential energy:
Potential energy determined
by the configuration of
electric charges.
Electric potential energy, PEe, is the measure of the
energy stored due to the configuration of a system of
charges. It reflects the positions (not the motion) of
the charges in the system.
The release of electric potential energy can be highly
visible. In a thunderstorm, clouds often accumulate a tremendous number of charged
particles in a configuration that stores huge amounts of electric potential energy. Part of
this energy can be released in the form of a lightning strike, a particularly dramatic
example of the effects of discharging PEe.
Recalling the fundamentals of gravitational potential energy may help you to understand
electric potential energy because the two are analogous. For example, the distance of
an apple above the Earth’s surface directly affects its gravitational potential energy, or
more precisely, the gravitational potential energy of the Earth/apple system. Lifting the
apple higher requires work í a force applied through a distance í and increases the
gravitational potential energy. Lowering the apple reduces the potential energy of the
system.
To apply these concepts to electric potential energy, consider the initial and final
configurations of opposite charges shown in the illustration of Concept 1. Initially, the
charges are touching. Then, the positive charge is moved to the right by an external
force while the negative charge on the left is held stationary. The work done on the
system by the force increases its potential energy.
In this chapter, since we are discussing potential energy in the context of electrostatics,
we focus on stationary charges. The charges are stationary in their initial and final
configurations, which means their KE does not change. Any work done on the charges
contributes only to changing their PEe. We state that as the first equation in Equation 1:
Work done on the charges equals the change of PEe. You can think of a direct
gravitational analogy: The work you do to raise an apple from one stationary position to
another equals its increase in PE.
Two charges with opposite signs attract each other, just as two masses do. Separate
two such charges, or two masses, and you increase their PEe. However, like charges
repel each other. It takes work to move them closer together, and this means their PEe
increases as they approach each other. The simulations you used in the introduction to
this chapter are designed to emphasize these points, and this may be a good time to try
them again. They show the similarities and differences in the PEe of similar
configurations of like or opposite charges.
So far, we have been discussing work done on a system of charges by an external
force. On the other hand, the fields of the particles themselves can do work on each
other, similar to what happens when an apple falls to the Earth under the pull of gravity.
This is referred to as work being done by the system. You see an example of this in the
illustration of Equation 1: After positive work done on the system separates the charges
and increases its potential energy, positive work done by the system pulls them back
together and decreases its potential energy again. This is directly analogous to the
relationship of work and gravitational potential energy: The gravitational potential
energy of a system decreases when two objects approach, as when an apple falls to
the Earth. We state this relationship between ǻPEe and work as the second equation in
Equation 1: The change in PEe equals the opposite of the work done by the system.
In either case í work done on the system or by the system í the work equals a force applied through a displacement. The electrostatic force
increases with the strength of the charges, and it decreases with distance. Be careful when you are asked to find the work done in changing
the separation between two charges. The amount of force constantly varies with distance, a fact you must account for when you calculate the
work. Calculus proves a useful tool for this, since it provides a technique for calculating work as the force varies over each small increment of
displacement.
The electrostatic force is conservative, and the work done by an electric field on charges is path independent. This means that the work done
by the field as a charged particle moves from one stationary position to another does not depend on the particle’s path between the positions.
For example, in the illustration of Concept 1, a horizontal force was exerted to push one particle directly away from the other to increase the
system’s potential energy. If the two particles had been moved from their indicated starting positions to their end positions by other paths
(perhaps involving extravagant zigzags and loops), the net work done and the final potential energy would have been the same. The
This Honda FCX automobile can cruise up to 350 km by using the electric
potential energy stored in its capacitors as a configuration of electric charge.Electric potential energy
Property of a system of charges
Depends on charge separation, strength