Electric Potential and Potential Difference
Simple Explanation
Electric potential at a point is the electric potential energy per unit charge a small positive test charge would have there. Potential DIFFERENCE between two points is simply the difference in potential between them — it determines how much work is done moving a charge between those points.
Why Do We Need It?
Potential difference (commonly called voltage) is one of the most practically important quantities in all of electricity — it's what drives current through circuits and is measured directly by a voltmeter.
Formula
Electric Potential (Point Charge)
V = kQ / r
Electric potential at a point measures the electric potential energy per unit charge that a small positive test charge would have at that point, due to a source charge Q.
- V
- — Electric potential, in volts (V)
- k
- — Coulomb's constant, ≈ 8.99 × 10⁹ N·m²/C²
- Q
- — Magnitude of the source charge, in coulombs
- r
- — Distance from the source charge, in metres
When to use it: Use to find the electric potential at a point a known distance from a point charge.
Worked Example
Finding electric potential from a point charge
Find the electric potential at a distance of 0.3 m from a charge of +5 × 10⁻⁶ C (k = 8.99 × 10⁹ N·m²/C²).
Why Does This Work?
Electric potential accounts for all the accumulated 'work done against the field' to bring a unit positive charge from very far away (where potential is defined as zero) to the point in question — since potential energy accumulates as you move closer to a source charge, this naturally gives a 1/r dependence, similar to gravitational potential energy near a mass.
Real-Life Example
Battery voltage
A 1.5 V battery maintains a fixed potential difference between its two terminals.
This 1.5 V potential difference is exactly what drives electric current through a connected circuit — it represents the energy given to each unit of charge as it moves from the battery's negative to positive terminal through the external circuit.
Practice
Find the electric potential at 0.5 m from a charge of +2 × 10⁻⁶ C (k = 8.99 × 10⁹ N·m²/C²).
HardCommon mistake
Confusing electric potential (a property of a POINT in space, in volts) with electric potential ENERGY (a property of a specific charge placed at that point, in joules) — potential energy equals charge times potential (PE = qV).
Quick Review
- V = kQ/r gives the electric potential at a distance from a point charge.
- Potential difference (voltage) is what drives current in circuits.
- Potential is energy PER UNIT CHARGE; multiply by charge to get actual potential energy.