What is electric potential, and how is it different from electric field?

Ask what is being measured. Electric potential, usually written V, is potential energy per unit charge: V = U/q. It describes a location’s energy-per-charge value and is a scalar, so it has no direction. Its unit is the volt, equal to J/C. Electric field, written E, is force per unit charge: E = F/q. It describes the force per charge and has direction; its unit is N/C. [S1]

Here’s a compact comparison:

Potential — energy per charge; scalar; volts (J/C). Electric field — force per charge; vector; N/C.

Potential difference describes how potential changes between locations; the field describes how potential changes in space. They are related, but not interchangeable.

Name the starting and ending points first. For a move from A to B, write the potential difference as ΔV = V_B − V_A. Reversing the move reverses the sign. A negative ΔV means the ending point has lower potential; it does not mean potential itself has a direction. [S1]

In electrostatics, the electric field points toward lower potential. The relationship is ΔV = −∫E·dl. The minus sign captures that relationship, and the dot product accounts for how much the displacement is along the field. Don’t infer the field’s direction from a potential value at just one point: compare how potential changes across a specified displacement.

Assume a uniform field along a straight 0.50 m displacement from A to B, and suppose the potential drops by 12 V: V_B − V_A = −12 V. Along that displacement, E = −ΔV/d, so the field component is −(−12 V)/(0.50 m) = 24 V/m, directed from A toward B. Since 1 V/m equals 1 N/C, that is also 24 N/C. The field points toward the lower-potential point, B. [S1]

This uniform-field relation applies here because the field is assumed uniform and aligned with the displacement. For a nonuniform field or a path not aligned with it, a single potential difference divided by distance does not generally give the full field vector; use the integral relationship. A potential value at only one point is not enough to establish the field.

Use a short setup before calculating:

1. Identify whether the question asks for potential V, potential difference ΔV, or field E.
2. Record the two locations and write ΔV = V_B − V_A in that order.
3. Check the units: volts for potential difference and N/C (or V/m in the uniform-field relation) for field.
4. Use E = −ΔV/d only when the field is uniform along the displacement, and state the direction separately.

For example, write: “From A to B, ΔV = V_B − V_A = [value] V. Assuming a uniform field along the displacement, E = −ΔV/[distance] = [value] V/m.” Then state the direction based on which point is at lower potential. If the information given cannot determine a field vector, say what is missing rather than treating potential as a direction.