Why are field lines always perpendicular to equipotentials?

The field is the negative gradient of the potential, E = −∇V. The gradient points where V changes fastest, while an equipotential is a direction in which V doesn’t change at all, so the two must be at right angles. That’s why moving a charge along an equipotential takes no work, and moving along a field line lowers the potential fastest. Turn both layers on and you can see they cross at 90° everywhere.

How does the spacing of field lines show field strength?

The number of lines leaving a charge is proportional to its charge, so the more lines cross a given length (an area, in 3D), the stronger the field — a picture of Gauss’s law. This tool assigns lines in proportion to |q|, so they crowd near charges and spread out far away. Equipotentials are drawn at equal steps ΔV, and since E ≈ ΔV / spacing, wherever they bunch up the field is strong too.

Why doesn’t the test charge follow the field lines?

A field line gives the direction of the force, and therefore the acceleration, not the velocity. Released from rest, the particle first accelerates along the line, but once it is moving its inertia carries it off a curved line. Only where lines are straight — on a dipole’s axis, or between parallel plates — does the path match the line. The simulation integrates m·a = qE with RK4 and reports how well kinetic plus potential energy is conserved.

What is the field halfway between two equal charges?

For two equal like charges, the fields at the midpoint are equal and opposite, so E = 0: it’s a null point where field lines split and never pass through. The potential there is not zero, though; it is 2kq/r, r being the distance to each charge. For a dipole (equal and opposite charges) it’s the reverse: V = 0 at the midpoint while the field is strong and points from + to −. Put the probe there to read both cases directly.

Why is the field between parallel plates uniform?

An infinite sheet with surface charge density σ produces a field of σ/(2ε₀) that doesn’t depend on distance. Two oppositely charged plates add to σ/ε₀ between them and cancel outside. The tool approximates the plates with two rows of point charges: in the middle the lines are parallel and evenly spaced and the equipotentials equally spaced, while near the ends the lines bow outward — the fringing field.

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⚡Electric Field Lines Simulator - Point Charges, Equipotentials, Coulomb Force

Place as many positive and negative point charges as you like and drag them around: the field and potential are recomputed live by superposition. Field lines leave each charge in proportion to its magnitude and are traced with RK4 until they reach an opposite charge; equipotentials are drawn at equal steps of V with marching squares, and you can overlay field vectors or a potential heat map. A probe reads |E|, its direction and V at any point, and below it you get the Coulomb force between any two charges, the net force on the selected one and the system's potential energy. Release a test charge to see its actual trajectory under the electric force, with energy conservation shown as an accuracy check.

Free · No sign-up · Runs in your browserLast updated: 2026-10-26

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How to use Electric Field & Potential Simulator

1Pick a preset (dipole, like charges, quadrupole, parallel plates…) or add positive and negative charges
2Drag charges to move them, edit their values in nC or μC, and toggle field lines, equipotentials, vectors and the heat map
3Hover or tap empty space to read the field and potential; choose two charges to see the force between them
4Switch to “release test charge”, tap the canvas and play the motion

FAQ

Why are field lines always perpendicular to equipotentials?: The field is the negative gradient of the potential, E = −∇V. The gradient points where V changes fastest, while an equipotential is a direction in which V doesn’t change at all, so the two must be at right angles. That’s why moving a charge along an equipotential takes no work, and moving along a field line lowers the potential fastest. Turn both layers on and you can see they cross at 90° everywhere.
How does the spacing of field lines show field strength?: The number of lines leaving a charge is proportional to its charge, so the more lines cross a given length (an area, in 3D), the stronger the field — a picture of Gauss’s law. This tool assigns lines in proportion to |q|, so they crowd near charges and spread out far away. Equipotentials are drawn at equal steps ΔV, and since E ≈ ΔV / spacing, wherever they bunch up the field is strong too.
Why doesn’t the test charge follow the field lines?: A field line gives the direction of the force, and therefore the acceleration, not the velocity. Released from rest, the particle first accelerates along the line, but once it is moving its inertia carries it off a curved line. Only where lines are straight — on a dipole’s axis, or between parallel plates — does the path match the line. The simulation integrates m·a = qE with RK4 and reports how well kinetic plus potential energy is conserved.
What is the field halfway between two equal charges?: For two equal like charges, the fields at the midpoint are equal and opposite, so E = 0: it’s a null point where field lines split and never pass through. The potential there is not zero, though; it is 2kq/r, r being the distance to each charge. For a dipole (equal and opposite charges) it’s the reverse: V = 0 at the midpoint while the field is strong and points from + to −. Put the probe there to read both cases directly.
Why is the field between parallel plates uniform?: An infinite sheet with surface charge density σ produces a field of σ/(2ε₀) that doesn’t depend on distance. Two oppositely charged plates add to σ/ε₀ between them and cancel outside. The tool approximates the plates with two rows of point charges: in the middle the lines are parallel and evenly spaced and the equipotentials equally spaced, while near the ends the lines bow outward — the fringing field.