Electric Potential Calculator

Calculate the electric potential (voltage) at a point in space due to one or more point charges.

ELECTRIC POTENTIAL
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Potential Energy
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Electric Field
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Work to Infinity
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Potential at 2r
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What Is Electric Potential?

Electric potential (also called voltage when measured as a difference) is the amount of electric potential energy per unit charge at a specific point in an electric field. It is a scalar quantity measured in volts (V), where 1 volt equals 1 joule per coulomb. Unlike the electric field which is a vector, potential has no direction, making it simpler to work with when analyzing complex charge distributions.

Electric potential is central to understanding circuits, capacitors, and energy storage. Batteries maintain a potential difference between their terminals, and this potential difference drives current through circuits. In nature, lightning occurs when the potential difference between clouds and ground becomes large enough to ionize the air.

The Formula

V = k × Q / r

Where V is the electric potential in volts, k = 8.9875 × 10&sup9; N·m²/C², Q is the source charge, and r is the distance from the charge. The potential energy of a test charge q at potential V is:

U = q × V

Potential vs Electric Field

PropertyElectric Potential (V)Electric Field (E)
TypeScalarVector
UnitVolts (V)N/C or V/m
Distance dependence1/r1/r²
SuperpositionAlgebraic sumVector sum

Equipotential Surfaces

An equipotential surface is a surface on which the electric potential is the same everywhere. No work is done when moving a charge along an equipotential surface. For a point charge, equipotential surfaces are concentric spheres centered on the charge. The electric field is always perpendicular to equipotential surfaces.

  • Moving along an equipotential surface requires zero work.
  • The spacing between equipotentials indicates field strength.
  • Conductors in equilibrium are equipotential surfaces.

Frequently Asked Questions

Can electric potential be negative?

Yes. A negative charge creates a negative potential in the surrounding space. This means a positive test charge placed at that point would have negative potential energy, indicating it would need external work to move it away from the negative source charge.

What is the potential at infinity?

By convention, the electric potential at infinity is defined as zero. This serves as the reference point for measuring potential. The potential at any finite distance from a charge is measured relative to this zero reference.

How does potential relate to voltage?

Voltage is technically a potential difference between two points. When we say a battery is "12 volts," we mean the potential difference between its terminals is 12 V. However, in everyday language, "potential" and "voltage" are often used interchangeably.