Electric Potential Calculator

Calculate electric potential, voltage, electric field strength, and potential energy using Coulomb's law.

Input charge magnitude, distance, and medium properties to determine electric potential characteristics and energy in electrostatic systems.

Examples

Click on any example to load it into the calculator.

Electron Potential

Electron Potential

Calculate the electric potential created by a single electron at 1 nm distance.

Charge: -1.6e-19 C

Distance: 1e-9 m

Dielectric: 1.0

Test Charge: 1.6e-19 C

Capacitor Potential

Capacitor Potential

Electric potential between parallel plates with 1 μC charge at 1 mm distance.

Charge: 1e-6 C

Distance: 0.001 m

Dielectric: 1.0

Test Charge: 1e-6 C

Potential in Water

Potential in Water

Electric potential of a 1 nC charge in water medium.

Charge: 1e-9 C

Distance: 0.01 m

Dielectric: 80.0

Test Charge: 1e-9 C

Potential in Glass

Potential in Glass

Electric potential of a 10 pC charge in glass medium.

Charge: 1e-11 C

Distance: 0.005 m

Dielectric: 4.5

Test Charge: 1e-11 C

Other Titles
Understanding Electric Potential Calculator: A Comprehensive Guide
Master the fundamental principles of electric potential and learn how to calculate voltage, electric fields, and potential energy in various physical scenarios. This guide covers everything from basic Coulomb's law to advanced applications in electrical engineering.

What is the Electric Potential Calculator?

  • Core Concepts
  • Coulomb's Law
  • Electric Potential vs. Electric Field
The Electric Potential Calculator is a powerful tool that implements Coulomb's law to calculate electric potential, voltage, electric field strength, and potential energy. It's based on the fundamental principle that electric charges create electric potentials that represent the work needed to bring a unit charge from infinity to a specific point. This calculator allows you to input charge magnitudes, distances, and medium properties to determine the complete electrostatic profile of a system.
Understanding Electric Potential
Electric potential (V) is a scalar quantity that represents the potential energy per unit charge at a point in space. It's measured in Volts (V) and is defined as the work done per unit charge to bring a test charge from infinity to that point. Unlike electric field, which is a vector quantity, electric potential is easier to work with in many applications because it's additive for multiple charges.
Coulomb's Law: The Foundation
Coulomb's law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. For electric potential, we use V = kQ/r, where k is Coulomb's constant (8.99 × 10⁹ N⋅m²/C²), Q is the source charge, and r is the distance from the charge.
Electric Potential vs. Electric Field
While electric potential (V) is a scalar quantity representing potential energy per unit charge, electric field (E) is a vector quantity representing force per unit charge. The electric field is the negative gradient of the electric potential: E = -∇V. Electric potential is often more convenient for calculations involving multiple charges or complex geometries because it's additive.

Key Physical Quantities:

  • Electric Potential (V): Measured in Volts (V), represents potential energy per unit charge
  • Electric Field Strength (E): Measured in N/C or V/m, represents force per unit charge
  • Potential Energy (U): Measured in Joules (J), the energy stored in the system
  • Dielectric Constant (εr): Unitless ratio that describes how a medium affects electric fields

Step-by-Step Guide to Using the Calculator

  • Input Parameters
  • Understanding Results
  • Common Applications
Using the Electric Potential Calculator requires understanding the physical parameters involved and their relationships. Follow this systematic approach to get accurate and meaningful results.
1. Determine the Source Charge
The source charge (Q) is the charge creating the electric potential. For electrons, use -1.6 × 10⁻¹⁹ C; for protons, use +1.6 × 10⁻¹⁹ C. For macroscopic objects, measure the charge in Coulombs. Remember that charge can be positive or negative, and the sign affects the electric potential value.
2. Measure the Distance
The distance (r) is measured from the source charge to the point where you want to calculate the electric potential. Use consistent units (typically meters). For very small distances (nanometers), use scientific notation. The distance must be positive and non-zero.
3. Specify the Medium
The dielectric constant (εr) describes how the medium affects the electric potential. In vacuum or air, εr = 1.0. In other materials, the dielectric constant reduces the electric potential. Common values include: water (80), glass (4.5), paper (2.2), and various plastics (2-4).
4. Analyze the Results
The calculator provides three key results: Electric Potential (V), Electric Field Strength (E), and Potential Energy (U). The electric potential tells you the voltage at that point relative to infinity. The electric field strength shows the force per unit charge. The potential energy gives the energy stored in the system when a test charge is present.

Common Dielectric Constants:

  • Vacuum/Air: εr = 1.0 (no effect on electric potential)
  • Paper: εr = 2.2 (reduces potential by factor of 2.2)
  • Glass: εr = 4.5 (reduces potential by factor of 4.5)
  • Water: εr = 80 (significantly reduces electric potential)

Real-World Applications and Engineering Uses

  • Electronics Design
  • Capacitor Applications
  • Particle Physics
Electric potential calculations are fundamental to many areas of physics and engineering, from designing electronic circuits to understanding particle behavior in accelerators.
Capacitor Design and Analysis
Capacitors are essential components in electronic circuits, and their behavior is governed by electric potential differences. The electric potential between capacitor plates determines the capacitance, breakdown voltage, and energy storage capacity. Engineers use electric potential calculations to optimize capacitor design for specific applications, from tiny integrated circuit capacitors to large power capacitors.
Semiconductor Device Physics
In semiconductor devices like transistors and diodes, electric potentials control the flow of charge carriers. The electric potential in the depletion region determines the device's electrical characteristics. Understanding electric potential distributions is crucial for designing efficient and reliable electronic components.
Particle Accelerators and Plasma Physics
In particle accelerators, electric potentials are used to accelerate charged particles to high energies. The electric potential difference determines the acceleration and the maximum energy particles can achieve. In plasma physics, electric potentials control the behavior of ionized gases, which is important for fusion research and plasma processing technologies.

Common Misconceptions and Error Prevention

  • Sign Conventions
  • Units and Scale
  • Potential Reference
Electric potential calculations can be tricky, and several common misconceptions can lead to errors. Understanding these pitfalls will help you use the calculator more effectively.
Misconception: Electric Potential is Always Positive
Electric potential can be positive or negative depending on the sign of the source charge. Positive charges create positive potentials, while negative charges create negative potentials. The sign is important for understanding the direction of electric fields and the behavior of charged particles.
Misconception: All Materials Have the Same Effect
Different materials have vastly different dielectric constants. Water, with εr = 80, dramatically reduces electric potential compared to air. This is why electrical equipment must be properly insulated and why capacitors use specific dielectric materials to achieve desired capacitance values.
Error: Ignoring Scale and Units
Electric potential calculations often involve very large or very small numbers. Always use appropriate units and scientific notation. For example, the charge of an electron (-1.6 × 10⁻¹⁹ C) is extremely small, while electric potentials can range from microvolts to megavolts depending on the application.

Important Reminders:

  • Always check units and use consistent systems (SI units recommended)
  • Remember that electric potential is a scalar - it's additive for multiple charges
  • The dielectric constant always reduces the electric potential
  • Electric potential is always relative to a reference point (usually infinity)

Mathematical Derivation and Advanced Concepts

  • Gauss's Law
  • Equipotential Surfaces
  • Potential Energy
Understanding the mathematical foundations of electric potential provides deeper insight into their behavior and applications.
Gauss's Law and Potential Calculations
Gauss's law provides an alternative method for calculating electric potentials, especially useful for symmetric charge distributions. It states that the electric flux through a closed surface is proportional to the total charge enclosed. For a point charge, Gauss's law leads to the same result as Coulomb's law: V = kQ/r.
Equipotential Surfaces and Visualization
Equipotential surfaces are surfaces where the electric potential is constant. For a point charge, these are concentric spheres. Electric field lines are always perpendicular to equipotential surfaces. This relationship is crucial for understanding electric field patterns and designing electrical systems.
Potential Energy and Work
The potential energy of a system of charges is related to the electric potential by U = qV, where q is the test charge and V is the electric potential. The work done to move a charge in an electric field is W = qΔV, where ΔV is the potential difference. This relationship is fundamental to understanding energy conservation in electrical systems.

Advanced Applications:

  • Multiple charge systems: Use superposition principle to add potentials
  • Continuous charge distributions: Integrate over charge density
  • Conductors: Electric potential is constant throughout a conductor
  • Dielectric materials: Polarization affects electric potential distribution