Electric Potential Energy
Electric potential energy is energy of a charge configuration. For point charges it depends on charge signs and separations, and the total for several charges is the scalar sum over distinct interacting pairs.
Electric Potential Energy: quick answer
Electric potential energy is energy of a charge configuration. For point charges it depends on charge signs and separations, and the total for several charges is the scalar sum over distinct interacting pairs. Electric potential energy belongs to the configuration, not to a single charge in isolation. The sign is physical: with zero at infinite separation, like-charge pairs have positive energy and opposite-charge pairs negative energy. Multi-charge systems require every distinct pair once.
Calculate electric potential energy only for configurations of four or fewer point charges; methods for extended charge distributions are outside this course scope.
What you should be able to explain and do
Use these as closed-note retrieval prompts before looking at the worked examples.
Interpret electric potential energy as work required to assemble a configuration from the chosen reference.
Use the signed two-point-charge potential-energy relationship.
Sum distinct pair energies for three- and four-charge systems.
Sketch and interpret U-versus-separation behavior for like and unlike charge pairs.
Key terms you need for this lesson
Definitions stay beside the model so a reader never has to leave the lesson to understand a prerequisite term.
configuration
configuration is the set of charge values and relative positions that defines the interacting system.
zero at infinity
zero at infinity is the conventional reference U=0 when isolated point charges are infinitely separated.
pair energy
pair energy is the electric potential-energy contribution associated with one distinct interacting pair.
assembly work
assembly work is external work required to bring charges quasistatically from the reference configuration to the stated configuration.
positive potential energy
positive potential energy is with the infinity reference, a configuration that requires positive external assembly work relative to infinitely separated charges.
negative potential energy
negative potential energy is with the infinity reference, a bound-like opposite-charge configuration below the zero-energy reference.
Know what each relationship means and when it applies
The equation, variables, vector/scalar nature, model condition and physical anchor belong together.
| Relationship / model | Variables & units | When to use it | Physical anchor |
|---|---|---|---|
U_E = q₁q₂/(4πεr) | U_E electric potential energy of the pair (J); q₁,q₂ charges (C); ε permittivity (F/m); r separation (m) | two point charges using zero potential energy at infinite separation | Like charges give positive U_E at finite separation; opposite charges give negative U_E with this reference. |
U_system = Σ_pairs q_iq_j/(4πεr_ij) | U_system total electric potential energy (J); each distinct charge pair is counted once | configurations of up to four point charges | For three charges, include the 1–2, 1–3 and 2–3 pair energies once each. |
W_ext,∞→configuration = U_E | W_ext work done by an external agent in assembling the configuration quasistatically from the zero reference (J); U_E resulting potential energy (J) | definition/interpretation of electric potential energy for a two-charge configuration | External work is positive when like charges are slowly brought closer from very far apart. |
What a strong diagram or graph must show
Translate the same physical model across words, diagrams, graphs and equations.
U-versus-r graph for like charges
positive curve approaching zero from above as r increases.
U-versus-r graph for unlike charges
negative curve approaching zero from below as r increases.
Pair table
list every distinct i–j interaction once before summing a multi-charge configuration.
Energy bar chart
compare electric potential energy before and after a rearrangement.
Change the model and inspect what must respond
Make a prediction first. Then move one control and explain the output using the governing relationship and representation.
Two-charge potential-energy explorer
Change charge signs and separation. The graph makes the sign and 1/r dependence visible using zero energy at infinite separation.
Two examples with the model choice shown
The goal is to expose the reasoning pathway, not only the final number.
Like-charge pair
Situation: Two +2.0 μC point charges are 0.30 m apart in vacuum.
Reasoning: Use U=kq₁q₂/r. The product q₁q₂ is positive, so U must be positive with zero at infinity.
U≈(8.99×10⁹)(4.0×10⁻¹²)/0.30≈0.120 J.
Three-charge accounting
Situation: Three point charges form a triangle.
Reasoning: The total energy is not one “net-charge” term. List the three unique pairs: 1–2, 1–3 and 2–3, calculate each signed pair energy, then add scalarly.
U_system=U₁₂+U₁₃+U₂₃; each pair is counted exactly once.
Recognize the physics before reaching for an equation
Use the cue to choose the model, connect it to nearby ideas, then reject any method whose assumptions do not match the situation.
What should trigger Topic 10.4?
Use electric potential energy when the energy belongs to an interacting charge configuration and depends on relative position.
How this idea fits the course
Topic 10.5 divides interaction energy by charge to define potential; Topic 10.7 uses potential-energy changes in conservation problems.
Scope check before solving
Calculate electric potential energy only for configurations of four or fewer point charges; methods for extended charge distributions are outside this course scope.
Turn this topic into measurable evidence
A strong investigation identifies variables, controls competing causes, repeats trials and chooses a graph from the predicted functional dependence.
Investigation target
Compare predicted electric-potential-energy changes with kinetic-energy changes in a charge-motion simulation.
Reasoning errors to eliminate
Repair the physical model before doing more arithmetic.
Six things you should be able to do before moving on
Use these as closed-note transfer prompts.
- I can define the core quantities and state whether each is vector or scalar.
- I can choose the governing relationship only after identifying source, probe and system boundary.
- I can explain every variable, unit, sign and reference convention.
- I can translate the situation into a field/equipotential/energy/geometry representation.
- I can predict direction or factor change before calculating.
- I can design or critique an experiment and justify a claim with data or physical principles.
Practice is kept on its dedicated pages
Finish the lesson first. Then open the separate topic bank when you want exam-style practice without replacing the teaching content above.
42 multiple-choice questions
Use the exact-topic MCQ bank to test model selection, representations, calculations and boundaries after learning the concept.
Open 42 Topic MCQs4 multipart free-response tasks
Use the exact-topic FRQ set for mathematical, representation, experimental and qualitative/quantitative reasoning.
Open 4 Topic FRQsTopic 10.4 FAQs
Why can electric potential energy be negative?
The zero is a chosen reference. Opposite charges at finite separation are below the infinite-separation reference, so their pair energy is negative.
Does negative potential energy mean negative total energy?
Not necessarily. Total system energy may include kinetic and other energy stores.
What happens to U for like charges as they separate?
Positive U decreases toward zero as separation increases.
What happens to U for opposite charges as they separate?
Negative U increases toward zero as separation increases.
How do I find energy for three charges?
Calculate the signed pair energy for each of the three distinct pairs and add them.
What reference is used here?
For isolated point charges, U=0 at infinite separation unless a problem explicitly defines another reference.