Electric Potential
Potential due to a point charge.
Formula
Live Calculator
MembersVariables
How it works
This formula gives the electric potential at a point a distance r from a single point charge q. It works because a charge creates an electric field, and the potential is the work needed per unit charge to bring a small test charge in from very far away; for a point charge, that work falls off as 1/r. The constant k sets the strength of the electric interaction and makes the units come out as volts.
When to use it
Use this when you need the potential caused by one isolated charge, or when approximating a small charged object as a point charge. It is especially useful in electrostatics problems involving energy, voltage differences, and combining potentials from several charges.
Worked example, step by step
A point charge of q = +3.0 × 10^-6 C is located in air. Find the electric potential at a point r = 0.20 m away. V = kq/r V = (8.99 × 10^9 N·m^2/C^2)(3.0 × 10^-6 C) / 0.20 m V = (2.697 × 10^4) / 0.20 V = 1.3485 × 10^5 V V ≈ 1.35 × 10^5 V
Common mistakes to avoid
- Forgetting that r must be measured from the charge to the point, not along a circuit path
- Using the wrong sign: a negative charge produces a negative potential
- Mixing up electric potential V with potential energy U, which would require multiplying by a test charge
Did You Know?
Voltage is electric potential energy per charge, the "pressure" that pushes current through a circuit.
Share this formula
More in Electricity & Magnetism
View allCoulomb's Law
IntermediateForce between two point charges.
Electric Field
BasicForce per unit charge at a point.
Field of a Point Charge
IntermediateElectric field around a point charge.
Electric Potential Energy
IntermediateEnergy of two interacting charges.
Gauss's Law
AdvancedElectric flux through a closed surface.
Parallel-Plate Capacitance
AdvancedCapacitance from plate area and separation.