Electric Potential

Electric potential is defined as the ratio of a charge's electric potential energy to the magnitude of the charge itself. While electric potential energy is the energy stored in a system of charges due to their positions, electric potential tells us how much potential energy exists per unit charge at a given location.

To see the distinction, imagine a positive test charge placed near a positive source charge. That test charge has a certain amount of electric potential energy, arising from the repulsive force between the two charges. The electric potential at that same point, however, doesn't depend on which test charge you place there — it depends only on the position and magnitude of the source charge, Q. Electric potential energy depends on the specific charge you're considering; electric potential describes the energy available to any charge placed at that location.

Key Takeaways

• Electric potential (V = U/q = kQ/r) is potential energy per unit charge at a location — unlike electric potential energy, it doesn't depend on which test charge is placed there.

• The SI unit of electric potential is the volt, equal to one joule per coulomb.

• Electric potential sits alongside electrostatic force, electric field, and electric potential energy as related but distinct ways of describing the same charge system.

• Potential difference (voltage), ΔV = Wab/q, measures the work needed to move a charge between two points — and is the quantity that drives current in electric circuits.

MCAT Callout — Worked Example: Electric Potential at a Point: A source charge of Q = +5×10⁻⁶ C sits 0.2 m from a point in space. The electric potential at that point is:

V = kQ/r = (8.99×10⁹)(5×10⁻⁶)/0.2 ≈ 2.25×10⁵ V

This value is the same no matter what test charge — or whether any test charge at all — occupies that point.

The Electric Potential Formula

V = U/q = kQ/r

where:

• V is the electric potential, measured in volts (V),

• U is the electric potential energy,

• q is the magnitude of the test charge,

• k is Coulomb's constant,

• Q is the source charge,

• r is the distance between the test charge and the source charge.

One volt is equivalent to one joule per coulomb — electric potential quantifies how much energy is associated with each coulomb of charge at a given location.

Electric Potential vs. Related Quantities

Electric potential is closely related to electrostatic force, the electric field, and electric potential energy, but each describes a different aspect of the same underlying system:

Notice the pattern: electric potential is related to electric field strength and potential energy, but it offers a different way of thinking about the energy landscape a charge creates — one centered on location, not on a specific pair of charges or a specific force.

Potential Difference (Voltage)

An important related concept is potential difference, more commonly called voltage. Consider two points, a and b, with electric potentials Va and Vb. The potential difference between them is:

ΔV = Vb − Va = Wab/q

where Wab is the work done in moving a charge q from point a to point b.

Voltage tells us how much work must be done to move a charge between two points — or, conversely, how much energy is available to be released if the charge is allowed to move between those points on its own. This concept becomes especially important in electric circuits, where the voltage between two points is exactly what drives the flow of current.

Common MCAT Mistakes

• Treating electric potential as if it depended on the test charge placed there. V is a property of the source charge and location alone — it's the same value whether a large test charge, a small one, or no test charge at all occupies that point.

• Forgetting that a volt is a joule per coulomb, not a joule alone. Electric potential is an energy-per-charge quantity — mixing it up with a raw energy unit leads to unit errors in circuit and electrostatics problems alike.

• Mixing up electric potential (V) with electric field (E). They're related but distinct: V is energy per unit charge (volts), while E is force per unit charge (N/C). Confusing the two — or their units — is a common source of calculation errors.

• Reversing the order in the potential difference formula. ΔV = Vb − Va, not Va − Vb. Getting the order backward flips the sign of the calculated potential difference (and the work associated with it).

MCAT-Style Concept Check

Question: A point charge of Q = −4×10⁻⁶ C is located 0.5 m from point P. What is the electric potential at point P?

• A) +7.19×10⁴ V

• B) −7.19×10⁴ V

• C) +3.60×10⁴ V

• D) −3.60×10⁴ V

Answer: B

Explanation: V = kQ/r = (8.99×10⁹)(−4×10⁻⁶)/(0.5) ≈ −7.19×10⁴ V. The negative sign follows directly from the negative source charge — the electric potential at that point is negative regardless of what test charge, if any, is placed there.

FAQ

What is electric potential?

Electric potential (V) is the ratio of a charge's electric potential energy to the magnitude of that charge — the amount of potential energy available per unit charge at a given location, given by V = U/q = kQ/r.

How does electric potential differ from electric potential energy?

Electric potential energy (U) depends on a specific pair of charges and their positions. Electric potential (V) depends only on the source charge and location — it's the same value no matter which test charge (or none) occupies that point.

What is the SI unit of electric potential?

The volt (V), equal to one joule per coulomb. It expresses how much energy is associated with each coulomb of charge at a given location.

What is potential difference (voltage) and why does it matter?

Potential difference, ΔV = Vb − Va = Wab/q, is the work required to move a charge between two points, divided by the charge. It's the quantity that drives current flow in electric circuits.