Electric Field Calculator

Calculate electric field strength, potential, and electrostatic force using Coulomb's law.

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

Examples

Click on any example to load it into the calculator.

Electron Field

Electron Field

Calculate the electric field 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 Field

Capacitor Field

Electric field 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

Field in Water

Field in Water

Electric field of a 1 nC charge in water medium.

Charge: 1e-9 C

Distance: 0.01 m

Dielectric: 80.0

Test Charge: 1e-9 C

Field in Glass

Field in Glass

Electric field 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 Field Calculator: A Comprehensive Guide
Master the fundamental principles of electrostatics and learn how to calculate electric fields, potentials, and forces in various physical scenarios. This guide covers everything from basic Coulomb's law to advanced applications in electrical engineering.

What is the Electric Field Calculator?

  • Core Concepts
  • Coulomb's Law
  • Electric Field vs. Electric Potential
The Electric Field Calculator is a powerful tool that implements Coulomb's law to calculate electric field strength, electric potential, and electrostatic forces. It's based on the fundamental principle that electric charges create electric fields that exert forces on other charges. This calculator allows you to input charge magnitudes, distances, and medium properties to determine the complete electrostatic profile of a system.
Understanding Electric Fields
An electric field is a region of space around a charged particle where other charged particles experience a force. The electric field strength (E) is defined as the force per unit charge experienced by a test charge placed in the field. It's a vector quantity, meaning it has both magnitude and direction. The direction of the electric field is defined as the direction a positive test charge would move if placed in the field.
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. Mathematically, F = k |q1 q2| / r², where k is Coulomb's constant (8.99 × 10⁹ N⋅m²/C²), q1 and q2 are the charges, and r is the distance between them.
Electric Field vs. Electric Potential
While the electric field (E) represents the force per unit charge, electric potential (V) represents the potential energy per unit charge. The electric field is the negative gradient of the electric potential: E = -∇V. Electric potential is a scalar quantity and is often easier to work with in many applications, especially when dealing with multiple charges or complex geometries.

Key Physical Quantities:

  • Electric Field Strength (E): Measured in N/C or V/m, represents force per unit charge
  • Electric Potential (V): Measured in Volts (V), represents potential energy per unit charge
  • Electrostatic Force (F): Measured in Newtons (N), the actual force between charges
  • 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 Field 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 field. 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 direction of the electric field.
2. Measure the Distance
The distance (r) is measured from the source charge to the point where you want to calculate the electric field. 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 field. In vacuum or air, εr = 1.0. In other materials, the dielectric constant reduces the electric field strength. 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 Field Strength (E), Electric Potential (V), and Electrostatic Force (F). The electric field strength tells you how strong the field is at that point. The electric potential gives you the work needed to bring a unit charge from infinity to that point. The electrostatic force shows the actual force on a test charge placed at that location.

Common Dielectric Constants:

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

Real-World Applications and Engineering Uses

  • Electronics Design
  • Capacitor Applications
  • Particle Physics
Electric field 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 fields. The electric field between capacitor plates determines the capacitance, breakdown voltage, and energy storage capacity. Engineers use electric field 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 fields control the flow of charge carriers. The electric field in the depletion region determines the device's electrical characteristics. Understanding electric field distributions is crucial for designing efficient and reliable electronic components.
Particle Accelerators and Plasma Physics
In particle accelerators, electric fields are used to accelerate charged particles to high energies. The electric field strength determines the acceleration and the maximum energy particles can achieve. In plasma physics, electric fields 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
  • Field Superposition
Electric field 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 Field Direction Doesn't Matter
While this calculator gives the magnitude of the electric field, direction is crucial in many applications. Electric field lines point away from positive charges and toward negative charges. When working with multiple charges, you must consider the vector nature of electric fields and use vector addition.
Misconception: All Materials Have the Same Effect
Different materials have vastly different dielectric constants. Water, with εr = 80, dramatically reduces electric field strength 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 field 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 field strengths can range from 10⁻⁶ N/C in weak fields to 10⁶ N/C in strong fields.

Important Reminders:

  • Always check units and use consistent systems (SI units recommended)
  • Remember that electric fields are vectors - direction matters in complex problems
  • The dielectric constant always reduces the electric field strength
  • Electric potential is always relative to a reference point (usually infinity)

Mathematical Derivation and Advanced Concepts

  • Gauss's Law
  • Field Lines
  • Potential Energy
Understanding the mathematical foundations of electric fields provides deeper insight into their behavior and applications.
Gauss's Law and Field Calculations
Gauss's law provides an alternative method for calculating electric fields, 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: E = kQ/r².
Electric Field Lines and Visualization
Electric field lines are imaginary lines that show the direction of the electric field at each point. They start on positive charges and end on negative charges. The density of field lines indicates the strength of the electric field. Field lines never cross, and they are always perpendicular to equipotential surfaces.
Potential Energy and Work
The electric potential energy of a charge in an electric field is given by U = qV, where q is the charge and V is the electric potential. The work done by the electric field when a charge moves from point A to point B is W = q(VB - VA). This relationship is fundamental to understanding electrical circuits and energy conservation.

Advanced Applications:

  • Electrostatic precipitators use electric fields to remove particles from air
  • Inkjet printers use electric fields to control droplet formation and direction
  • Mass spectrometers use electric fields to separate ions by mass-to-charge ratio
  • Electron microscopes use electric fields to focus electron beams