Electric Potential
Electric potential is a scalar energy-per-charge field. Potentials from point charges add algebraically, equipotential lines are perpendicular to electric-field vectors, and electric field points toward decreasing potential.
Electric Potential: quick answer
Electric potential is a scalar energy-per-charge field. Potentials from point charges add algebraically, equipotential lines are perpendicular to electric-field vectors, and electric field points toward decreasing potential. Potential is often easier than force because it is scalar. But “scalar” does not mean “always positive”: source-charge signs matter. The most important representation translation is between equipotential maps and field vectors—E is perpendicular to equipotentials and points toward decreasing V.
Calculate electric potential only for configurations of four or fewer point charges unless high symmetry simplifies the situation. Do not use extended-charge integration methods; remember that potential is scalar and electric field is vector.
What you should be able to explain and do
Use these as closed-note retrieval prompts before looking at the worked examples.
Define electric potential and potential difference as energy per unit charge.
Use scalar superposition for potentials from several point charges.
Translate between equipotential maps and electric-field direction/relative magnitude.
Explain why conductors in electrical contact redistribute charge until their surfaces share one potential.
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.
volt
volt is one joule per coulomb, the SI unit of electric potential and potential difference.
equipotential line
equipotential line is a line joining points with equal electric potential, so displacement along it has no electric-field component.
potential gradient
potential gradient is the spatial rate and direction of potential change; stronger field corresponds to a steeper decrease in potential.
scalar superposition
scalar superposition is algebraic addition of signed potential contributions rather than vector addition.
electrical contact
electrical contact is a conducting connection that permits mobile charge to redistribute between conductors.
potential reference
potential reference is the chosen zero of V, commonly V=0 at infinity for isolated point-charge calculations.
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 |
|---|---|---|---|
V = U_E/q_test | V electric potential (V=J/C); U_E interaction energy involving the test charge (J); q_test test charge (C) | definition of electric potential at a point | If a +2 C test charge would have 6 J of electric potential energy at a point, that point is at 3 V. |
V = Σ_i Q_i/(4πεr_i) | V total potential (V); Q_i source charges (C); r_i distance from each source to the point (m); ε medium permittivity | up to four point charges, or more in high-symmetry cases, using zero potential at infinity | A positive and negative source can give zero potential at a point even when the electric field there is not zero. |
E_avg,parallel = −ΔV/Δs | E_avg component of average electric field along displacement (V/m=N/C); ΔV=V_f−V_i (V); Δs displacement along the field coordinate (m) | relating potential change to the average field along a chosen direction; in a uniform field this becomes exact along that line | Moving in the electric-field direction lowers electric potential; closely spaced equipotentials indicate a stronger field. |
What a strong diagram or graph must show
Translate the same physical model across words, diagrams, graphs and equations.
Equipotential map
closely spaced neighboring lines indicate a larger magnitude of electric field.
Field vectors
perpendicular to equipotential lines and pointing from higher toward lower V.
V-versus-position graph
slope sign is opposite the field component along that coordinate.
Multi-charge table
add signed scalar potential contributions even when field vectors cancel or reinforce differently.
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.
Potential and field at the same point
Use two source charges and one observation point. Compare scalar V with signed x-component E to see why V=0 does not imply E=0.
Two examples with the model choice shown
The goal is to expose the reasoning pathway, not only the final number.
Zero potential, nonzero field
Situation: Equal +Q and −Q charges are separated symmetrically. Consider the midpoint.
Reasoning: The scalar potentials +kQ/r and −kQ/r cancel. The field vectors, however, point in the same direction from +Q toward −Q.
At the midpoint V=0 while E≠0. This is a central field-versus-potential distinction.
Uniform-field potential change
Situation: Across 0.020 m in the +x direction, potential decreases by 600 V in an approximately uniform field.
Reasoning: Along x, E_x=−ΔV/Δx. The negative potential change gives a positive field component.
E_x=−(−600)/0.020=3.0×10⁴ V/m in +x.
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 10.5?
Use electric potential when the target is energy per unit charge, voltage, equipotentials, or scalar superposition.
How this idea fits the course
Potential links fields in 10.3 to energy in 10.4 and becomes the voltage language used for capacitors and circuits.
Scope check before solving
Calculate electric potential only for configurations of four or fewer point charges unless high symmetry simplifies the situation. Do not use extended-charge integration methods; remember that potential is scalar and electric field is vector.
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
Map voltage on conductive paper, draw equipotentials, and estimate electric-field direction from the map.
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 10.5 FAQs
What is the difference between electric potential and electric potential energy?
Potential V is energy per unit charge at a location; potential energy U depends on the charge placed in that potential and the chosen interacting system.
Is electric potential a vector?
No. It is scalar, so signed contributions add algebraically.
Which way does electric field point on a potential map?
Perpendicular to equipotential lines and toward decreasing potential.
Can potential be zero while field is nonzero?
Yes, for example at the midpoint of equal opposite point charges.
Why do touching conductors reach the same potential?
Mobile electrons redistribute through the electrical connection until no potential difference remains to drive further net redistribution.
What do tightly spaced equipotential lines mean?
A larger magnitude of electric field because potential changes more rapidly with distance.