Electricity · Physics

Voltage is energy per unit charge.

Electric potential gives an energy-based way to solve electrostatics. It connects directly to work done by electric forces and links to the electric field through spatial change.

This topic

Electric Potential and Potential Energy

Distinguish V from U, compute potential differences, interpret work, and connect E to V.

Definitions

Potential vs potential energy

Electric potential energy U belongs to a specific charge configuration. Electric potential V is the potential energy per unit charge at a location.

U depends on the test charge q
V is defined as V = U/q
Units: U in joules, V in volts (J/C)
Why V is a property of the field/source charges

Voltage

Potential difference

Potential difference (voltage) between two points tells you how much potential energy changes per unit charge when moving between those points.

ΔV = V_final − V_initial
Meaning: energy change per coulomb
Only differences matter (choice of zero reference)
Sign matters for positive vs negative charges

Work

Work done by electric forces

Electric forces are conservative in electrostatics. That means the work they do depends only on initial and final points, not the path.

W_electric = −ΔU
For a charge q: ΔU = qΔV
Path independence (electrostatics)
Interpreting signs: when field does positive work

Connection

Relationship between E and V

The electric field points in the direction of greatest decrease of potential. In one dimension, the field is the negative slope of V versus position.

Field points “downhill” in V
For 1D: E = −dV/dx
For uniform field: ΔV = −EΔx (along the field)
Why equipotentials are perpendicular to E (next topic)

Practice

Practice & Exercises

Practice interpreting voltage as energy per charge and connecting it to work and field direction.

Compute ΔU from q and ΔV
Sign reasoning: positive vs negative charges
Work-energy questions for charges moving in fields
Find E from V(x) graphs in 1D
Exam-style potential and energy sets