Point Charge Electric Field Calculator

Formula: Point-charge electric field model

This point-charge electric field calculator keeps a fixed source charge Q at the center of the canvas and releases a test charge q with mass m from the starting position (x₀, y₀). The blue radial lines show the direction of the electric field around the source, and the orange point shows the test charge as Coulomb's law pulls or pushes it through the plane. All values are interpreted in SI units: coulombs for charge, kilograms for mass, meters for position, seconds for time, joules for energy, and newtons per coulomb for field strength.

Core equations for a point-charge field

For a single ideal point charge, the field magnitude grows with the size of Q and falls off with the square of the distance from the origin. That is why moving the test charge a little farther away can have a much bigger effect on the displayed field than changing the charge by a small amount:

Here k = 8.9875517923 × 10⁹ N·m²/C² and r is the distance from the source charge to the test charge. The force on the moving charge is F = qE, so the sign of q matters just as much as the sign of Q. In vector form, the animation advances the motion using

When Qq is positive, the interaction is repulsive and the orange test charge moves away from the source. When Qq is negative, the interaction is attractive and the charge heads inward. The simulator also keeps track of kinetic energy KE = 1/2 mv² and electric potential energy PE = kQq/r, which makes it easy to see how speed and position trade off as the particle moves.

Choosing point-charge inputs

• Q (C): the fixed source charge at the origin. Positive values make the field point outward; negative values reverse the arrows and draw a positive test charge inward.
• q (C): the moving test charge. Its sign determines whether the source repels it or attracts it, and its magnitude sets how strongly the field pushes on it.
• m (kg): the test-charge mass. A smaller mass responds more quickly to the same electric force, while a larger mass moves more sluggishly.
• x₀, y₀ (m): the starting coordinates of the test charge. Pick a point away from the origin, because the ideal point-charge model becomes singular exactly at the source.
• Δt (s): the integration time step used by the animation. Smaller values usually produce smoother, more accurate trajectories, while larger values move faster but can drift more easily.

Worked point-charge example

With the default point-charge values Q = 1e-6 C, q = 1e-6 C, m = 1e-3 kg, and an initial separation of r = 0.10 m, the calculator reports an electric field of about 8.99 × 10⁵ N/C. That gives a force of about 0.899 N on the test charge and an initial acceleration of about 899 m/s². The starting potential energy is 0.0899 J, and because both charges are positive, the test charge begins by accelerating away from the origin rather than toward it. If the test charge had the opposite sign at the same distance, the field magnitude would stay the same but the motion would reverse, which is the easiest way to sanity-check the sign handling in a point-charge setup.

Point-charge comparison table

Reading the point-charge output

The result panel reports simulation time, distance from the source, and relative energy drift, which is the quickest way to judge whether your chosen time step is keeping the point-charge motion numerically stable. The kinetic-energy bar and potential-energy bar compare the instantaneous kinetic energy with the magnitude of electric potential energy, so attractive cases with negative potential energy still show a readable balance instead of a confusing sign flip. The CSV button exports time, position, velocity, kinetic energy, and potential energy for later graphing, and the caption under the canvas summarizes the particle's current separation from the source charge. If the drift starts to grow or the path looks jumpy near the center, lowering Δt is usually the first fix to try.

Point-charge model limitations

This point-charge electric field calculator uses one ideal source charge and one moving test charge, so it is best treated as a Coulomb's-law teaching model rather than a full physics engine. It does not include radiation, relativity, collisions, boundaries, or the influence of any additional charges. The field is undefined exactly at the source, which is why the simulation pauses if the particle gets too close to the origin. Very large charges, very small masses, or a time step near the upper end of the allowed range can make the motion look abrupt or produce visible numerical error, so the safest way to improve accuracy is to reduce Δt and keep the start point well away from the singularity.

How to use this point-charge calculator

1. Enter Q (C) to set the fixed source charge at the center of the field and note that its sign controls whether the field points outward or inward.
2. Enter m (kg) to control how quickly the test charge responds to the electric force; smaller masses accelerate more sharply in the same field.
3. Enter x₀ (m) and y₀ (m) to place the moving charge away from the origin, since the ideal point-charge field cannot be evaluated at r = 0.
4. Enter q (C) so the simulator can decide whether the source attracts or repels the moving charge and how the potential energy term should change.
5. Set Δt (s) to a step size that balances smooth motion and accuracy, then press Play and compare a second run with a changed sign, mass, or starting point to see how the point-charge field responds.