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PHYSICS • ELECTROMAGNETISM

Coulomb’s Law & Electric Field Mapping

Change two point charges and move a probe through their field to inspect vector superposition, potential and source-source force.

● FIELD SUPERPOSITIONPoint charges
Field magnitude
Potential
Charge force
Interaction

Reasoning inspector

live model state
Eₓ—
Eᵧ—
|E|—
Electric potential—
Charge-pair force—
Interaction—
Probe distance r₁—
Probe distance r₂—

Add fields as vectors

Every point charge contributes an inverse-square electric field. The net field is the vector sum of those contributions, while electric potential adds as a signed scalar.

LEARN WITH THE SIMULATION

Understand Coulomb’s Law & Electric Field Mapping by experimenting.

START HERE

Electric fields and electric potential obey superposition, but they do not combine in the same mathematical way. This laboratory places two point charges in a plane, maps equipotential contours and vector-field directions, and lets a movable probe report Ex, Ey, field magnitude and scalar potential. A field-null challenge makes the central distinction testable: vector contributions can cancel even when the scalar potential is not zero, and the reverse can also occur.

BUILD THE IDEA

What you should understand first

  • Add electric-field contributions component by component as vectors.
  • Add electric potential contributions algebraically as signed scalars.
  • Use inverse-square field scaling and source geometry to reason about cancellation points.
  • Separate the force between the source charges from the field measured at the independent probe location.

TRY IT YOURSELF

Can the net electric field be nearly zero at a point where electric potential is clearly nonzero?

  1. Set two equal same-sign charges and place the probe near the midpoint.
  2. Reduce the field magnitude by moving onto the symmetry point and inspect Ex and Ey separately.
  3. Read the electric potential at the same location.
  4. Switch one source charge to the opposite sign and compare how the field and potential cancellation patterns change.
Read the visual:

For equal same-sign charges, the midpoint field vectors oppose and cancel while their positive scalar potentials add. For equal opposite charges, the midpoint potential can cancel while the field contributions point in the same direction. The two zero conditions therefore describe different mathematics.

WHY IT WORKS 01

Field cancellation requires both vector components to cancel

Each point charge contributes a field vector proportional to q/r² in the radial direction. A true field-null point requires the summed x component and summed y component to vanish simultaneously. Symmetry can make this easy to predict, as with equal same-sign charges at their midpoint, but unequal charges generally move the cancellation point away from simple geometric centers.

WHY IT WORKS 02

Potential superposition ignores direction

Electric potential from a point charge is proportional to q/r and carries the sign of the source charge but no vector direction. Contributions therefore add as ordinary signed numbers. This is why equal opposite charges can produce V = 0 on a symmetry set while the corresponding electric-field vectors reinforce rather than cancel.

WHY IT WORKS 03

Contours and field vectors encode the same scalar field differently

Equipotential contours join points with equal electric potential. The electric field points in the direction of steepest decrease of potential, so in an ideal continuous map field lines cross equipotential contours at right angles. The simulator samples and draws these quantities numerically, providing a visual bridge between the scalar potential landscape and its vector gradient.

DO NOT MIX THESE UP

Common misconception

Zero electric potential does not imply zero electric field, and zero electric field does not imply zero potential. Potential is a scalar sum while field is a vector sum. The source-charge force shown by the model is the mutual Coulomb force at their separation; it is not the force on the probe unless a test charge is separately specified.

PRACTICE CHALLENGE

Can you create a low-field probe location and then determine whether that location is also an equipotential zero?

  • Choose a target maximum field magnitude.
  • Adjust source signs, magnitudes or probe position until the field target is met.
  • Inspect Ex and Ey to verify vector cancellation rather than relying only on |E|.
  • Compare the potential value at the same point and explain why it need not be zero.
Reveal the reasoning

A low-field point occurs when the vector contributions nearly cancel in both components. Potential is a separate scalar sum, so its value depends on signed q/r contributions rather than directional cancellation. Equal same-sign charges at a symmetric midpoint provide a clear example of E ≈ 0 while V remains nonzero.

MODEL BOUNDARIES

What this simulation assumes

Every simulation simplifies reality or a mathematical system. These are the assumptions and limits to keep in mind while interpreting the results.

Model assumptions

  • Charges are stationary point charges in vacuum and the field is evaluated in a two-dimensional slice.
  • Electric-field vectors and scalar electric potentials obey linear superposition.
  • The reported source-source force uses Coulomb's inverse-square law at the selected separation.

Model limitations

  • Finite charge distributions, dielectric materials, conductors, image charges and relativistic effects are omitted.
  • Vector arrows are normalized for readability and do not encode field magnitude by length.

CONNECT IT

Where this matters

  • Electrostatic field mapping
  • Charge sensing and electrode design
  • Reasoning about equilibrium points
  • Preparing for electric potential energy and capacitor fields

WORDS THAT MATTER

Key vocabulary

Electric field
Vector force per unit positive test charge at a point in space.
Electric potential
Scalar electric potential energy per unit charge.
Superposition
Rule that total response is the sum of contributions from individual sources.
Equipotential
Curve or surface along which electric potential is constant.
Field-null point
Location where vector electric-field contributions sum to zero.