Electric Potential Energy
High-Yield Summary
- Electric potential energy: U = kQq/r — energy stored due to the relative positions of two charges, analogous to gravitational PE.
- U also equals the work needed to bring a charge from infinitely far away to its current point (same unit as work: joules).
- Like charges (both + or both −) → U is positive (repulsive; energy must be added to bring them closer).
- Unlike charges (one +, one −) → U is negative (attractive; energy is released as they approach).
- U describes a pair of charges — distinct from electric potential (V), which describes a single location independent of any specific charge.
Electric Potential Energy
U = kQq/r
- U = Electric potential energy
- k = Coulomb's constant, 8.99×10⁹ N·m²/C²
- Q, q = Magnitudes of the two charges
- r = Distance between the charges
- Derived from Fe = kqQ/r² and W = Fd·cos θ, setting d = r with force and displacement parallel.
Sign of U by Charge Combination
| Charge Pair | Sign of U |
|---|---|
| Like charges (+/+ or −/−) | Positive — repulsive; energy input needed to bring together |
| Unlike charges (+/−) | Negative — attractive; energy released as they approach |
Common MCAT Trap
- Don't confuse electric potential energy (U, a pair-of-charges quantity) with electric potential (V, a single-location quantity) — they look similar but describe different things.
- A negative U doesn't mean 'less energy exists' in an absolute sense — it signals an attractive interaction where energy would be released on approach.
Quick Recall
Two like charges are brought closer together. What happens to U, and why?
What's the other way to define electric potential energy, besides U = kQq/r?