Electric Field & Potential Mapper Physics

Click to place + charge
Shift+click for - charge
Drag test charge (green dot)
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What is the Electric Field & Potential Mapper?

Quick Answer: An interactive electrostatics sandbox. Place positive/negative point charges, then see the electric field lines, equipotential contours, and a movable test charge. The potential and field at any point are computed live. Ideal for understanding Coulomb's law, superposition, and field patterns.

Theory of Electric Fields and Potential

The electric field E at a point due to a point charge q is E = k q / r2 (radially outward for positive). For multiple charges, fields superimpose as vectors. Electric potential V = k q / r (scalar, with sign). Equipotential surfaces are perpendicular to field lines. The test charge experiences force F = qtest E. This simulation computes the net field and potential at every pixel (or sampled point) and draws field lines via streamline integration from positive charges.

Step-by-Step Examples

Example 1: Dipole Field

  1. Click to place a positive charge (red) and a nearby negative charge (blue) of equal magnitude.
  2. Field lines emerge from the positive and terminate at the negative. Equipotential lines (cyan) show closed loops around each charge.
  3. Drag the green test charge to see how the force vector changes direction.

Example 2: Uniform Field Approximation

  1. Place two parallel lines of opposite charges (a crude capacitor). Field lines become nearly straight and parallel in the central region.
  2. Toggle the vector grid to see the uniform direction.

Example 3: Single Charge

  1. Clear all, add one positive charge. Field lines radiate outward, equipotential lines are concentric circles.
  2. Move test charge around; the info panel shows distance, potential, and field magnitude.

Frequently Asked Questions

How do I place a charge?

Click on the canvas to place a positive charge. Hold Shift and click to place a negative charge. Use the buttons to add at random positions.

What does the test charge do?

The green dot is a small positive test charge. Drag it to any point to see the electric force (arrow) and the potential value at that spot. It does not affect the field from the fixed charges.

Why are some field lines incomplete?

Field lines are traced from each positive charge outward. If they don't reach a negative charge, they stop at the canvas boundary or after a set length. Negative charges act as sinks.

How are equipotential lines drawn?

The potential is computed on a fine grid. Contour lines are extracted at regular intervals (e.g., every 5 V) using a simple threshold-crossing algorithm along grid edges.

Is this a full 3D field?

This is a 2D cross-section. For three-dimensional configurations, the field would fall off as 1/r2 identically, but the geometry is planar.