Electric Potential Energy
The energy stored in an arrangement of charges.
Lesson at a glanceShow the key points
- ΔU = −(work done by electric forces).
- U(r₂) − U(r₁) = (q₁q₂/4πε₀)(1/r₂ − 1/r₁) (29.5); with U(∞) = 0, U = q₁q₂/4πε₀r (29.6).
- Depends only on separation; for many charges, sum over all pairs.
Push two like charges together and you do work against their repulsion. That work is stored as electric potential energy, ready to fling them apart again.
Defining the change
When charges in a system move, the electric forces between them may do work. The change in electric potential energy is defined as the negative of the work done by the electric forces as the configuration changes.
Hold q₁ fixed and move q₂ from distance r₁ to r₂. In a small step dr the electric force does work (q₁q₂/4πε₀r²) dr; adding up,
Choosing zero at infinity
Taking U = 0 when the charges are infinitely far apart:
For three or more charges, add the potential energies of every pair.
Three charges of 5.0 µC sit at the corners of an equilateral triangle of side 15 cm. How much work must you do to pull them infinitely far apart (slowly)?
Find the potential energy of an electron and a proton 0.053 nm apart (as in a hydrogen atom), in electronvolts.
- 1ΔU = −(work done by electric forces).
- 2Two charges: U = q₁q₂/4πε₀r, zero at infinite separation.
- 3Many charges: sum over all pairs.
Check yourself
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