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Potential energy of charges
Intermediate
Energy stored in a system of charges.
U = kq₁q₂/rThe energy to assemble point charges is U = kq₁q₂/r for a pair, and the sum over all pairs for many. Positive for like charges (repulsion).
Three equal charges at triangle corners: 3 pair terms.
Count each pair only once.
In more detail
The potential energy of two point charges is U = kq1q2/r. Like charges have positive energy and repel, while unlike charges have negative energy and attract.
Real-world uses
- Calculating the energy needed to assemble ions in a crystal.
- Explaining bond energies in molecules.
- Chemists use the potential energy of point charges to estimate the energy holding ions together in a crystal.
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Frequently asked questions
Why is the energy negative for unlike charges?
Because they attract, so the energy is lower when they are close together.
How is it found for several charges?
Sum the pairwise energies, counting each pair once.
Why is the energy of two like charges positive?
Like charges repel, so bringing them closer requires work, which increases the stored energy.
Related topics in Electrostatics
Equipotential surfaces · Relation of E and V · Electron volt · Capacitor · Parallel-plate capacitor · Capacitors in series