Definition
Electric potential at a point is the electric potential energy per unit positive charge, V = W/q, measured in volts. Potential is a scalar field defined relative to a chosen reference point and is related to the electric field by E = −∇V.
Learning objectives
- Define electric potential and explain why it is measured in volts.
- Distinguish electric potential from potential difference and potential energy.
- Calculate potential from work and charge.
- Relate potential difference to electric field strength in a uniform field.
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Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
Electric potential tells you how much energy each unit of charge would have at a point. If a point has a potential of 12 V, then every coulomb of positive charge placed there has 12 joules of potential energy relative to the reference point. A battery terminal at 12 V is like the top of a hill for charge: charge is pushed from the higher potential to the lower potential.
We almost never measure absolute potential. Instead we measure a difference between two points, which is what a voltmeter does. The negative terminal of a car battery is normally used as the 0 V reference, so we describe the positive terminal as 12 V. The choice of reference does not change any physical result.
We almost never measure absolute potential. Instead we measure a difference between two points, which is what a voltmeter does. The negative terminal of a car battery is normally used as the 0 V reference, so we describe the positive terminal as 12 V. The choice of reference does not change any physical result.
Intermediate How it behaves in a circuit
Electric potential is a scalar, so potentials from several charges add algebraically, with their signs, without vector arithmetic. For a point charge Q, the potential at distance r from it is V = kQ/r, taking V = 0 at infinity. A positive charge produces positive potential and a negative charge produces negative potential. A surface on which the potential is the same everywhere is an equipotential surface.
The potential difference between two points is the work done per unit charge moving between them, and the electric field points in the direction of decreasing potential. In a uniform field, the potential falls linearly with distance along the field, giving ΔV = E × d. A voltmeter measures this difference and draws only a tiny current because of its high input resistance.
The potential difference between two points is the work done per unit charge moving between them, and the electric field points in the direction of decreasing potential. In a uniform field, the potential falls linearly with distance along the field, giving ΔV = E × d. A voltmeter measures this difference and draws only a tiny current because of its high input resistance.
Advanced Limits, assumptions, engineering detail
The potential formulation often simplifies field problems because it replaces a vector field with a scalar one: solving Laplace’s or Poisson’s equation for V, then taking E = −∇V, is a standard approach for boundary-value problems. In circuits, node potentials are the unknowns in nodal analysis, and the arbitrary reference node (ground) removes the constant offset ambiguity. Potential is continuous through space but can jump across the ideal model of a source; real sources have internal impedance, so the terminal voltage falls under load.
Potential energy is only defined for a charge configuration, whereas potential belongs to the field itself. In a capacitor, energy is stored in the field, with energy density ½εE². This distinction matters when fields change in time and when electromagnetic energy propagates through space rather than along conductors.
Potential energy is only defined for a charge configuration, whereas potential belongs to the field itself. In a capacitor, energy is stored in the field, with energy density ½εE². This distinction matters when fields change in time and when electromagnetic energy propagates through space rather than along conductors.
Formulas and variables
Potential from work and charge
V = W / q
V Electric potential · V
W Work or potential energy · J
q Charge · C
30 J of work to move 0.50 C gives V = 30 / 0.50 = 60 V.
Potential near a point charge
V = k × Q / r
V Electric potential · V
k Coulomb constant · ≈ 8.99 × 10⁹ N·m²/C²
Q Source charge · C
r Distance from the charge · m
A 2.0 µC charge at 0.30 m gives V = 8.99 × 10⁹ × 2.0 × 10⁻⁶ / 0.30 ≈ 59.9 kV.
Potential difference in a uniform field
ΔV = E × d
ΔV Potential difference · V
E Electric field strength · V/m
d Distance along the field · m
A field of 500 V/m over 0.040 m gives ΔV = 20 V.
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Electric potential | V | volt (V) |
| Potential energy | W | joule (J) |
| Charge | q | coulomb (C) |
| Electric field | E | volt per metre (V/m) |
Worked examples
Worked example
Potential from energy per charge
Problem. Moving 0.50 C between two points requires 30 J of work. What is the potential difference?
Solution. V = W / q = 30 J / 0.50 C = 60 V.
The potential difference is 60 V.
Worked example
Potential of a point charge
Problem. Calculate the potential 0.30 m from a point charge of 2.0 µC, with zero potential at infinity.
Solution. V = kQ/r = 8.99 × 10⁹ × 2.0 × 10⁻⁶ / 0.30 = 17,980 / 0.30 ≈ 59,933 V.
V ≈ 59.9 kV.
Practical applications
- Nodal analysis of circuits
- Battery and cell terminal voltages
- Capacitor energy storage
- Electrostatic shielding and equipotential bonding
Automotive applications
Automotive electrics use the chassis as the reference potential, conventionally called ground or 0 V. Every module measures voltages relative to this reference, so a poor chassis connection shifts the reference and corrupts sensor readings. Voltage-drop testing of grounds is therefore part of systematic electrical diagnosis.
Industrial applications
Industrial distribution systems define a reference and distributed equipotential bonding so that touch voltages stay controlled. In three-phase systems, phase-to-neutral and phase-to-phase potentials are different values, and the same physical insulation may be stressed differently depending on the earthing arrangement of the installation.
Measurement procedure
- A voltmeter measures potential difference, so both probes must contact the two points of interest.
- The meter’s high input resistance means it draws very little current, but it still loads very high-impedance circuits.
- Ground references can differ between equipment; measure between the actual points rather than assuming earth is one node.
- For safety, select a meter and leads with a voltage and category rating suitable for the circuit.
Common mistakes
- Confusing potential with potential energy: potential is energy per unit charge, measured in volts.
- Believing potential has an absolute value: only differences are measurable and physically meaningful.
- Treating potential as a vector: it is a scalar and adds algebraically with sign.
- Assuming a voltmeter reads the same voltage regardless of where its reference probe is placed.
Safety considerations
- Treat a conductor at a potential different from earth as live until proved otherwise.
- Use test leads and meters rated for the installation category and voltage involved.
- Do not rely on a single meter indication; verify on a known good source and re-verify after the measurement.
Frequently asked questions
What is the difference between electric potential and voltage?
Voltage is a potential difference between two points. Electric potential is the value at a single point relative to a chosen reference.
Why is earth often taken as zero volts?
The earth is a convenient, widely available reference, and bonding to it keeps touch voltages and fault behaviour predictable.
Can a point have negative potential?
Yes. Potential is relative to the chosen zero, so a point can be at a lower potential than the reference and therefore negative.