Coulomb's Law Simulator

What Is the Coulomb's Law Simulator?

Adjust Two Charges and Watch the Force Flip Sign

Gravity only ever pulls, yet electric charge follows the same inverse-square geometry while doing something gravity never can — it can attract or shove apart. This simulation lets you feel that split. Nudge the Charge q1 and Charge q2 sliders through positive and negative values and the Interaction readout swaps between attract and repel: like signs repel, opposite signs pull together, exactly as F = k·|q1·q2| / r² predicts. The Coulomb constant k ≈ 8.99×109 N·m²/C² sits fixed on the panel; you are steering the charges and their gap, not the vacuum around them.

The Separation r slider is where intuition usually breaks. Because force scales as 1/r² and not as 1/r, halving the gap does not double the force — it quadruples it, and doubling the gap drops the force to a quarter. Slide r and read the number: the response is far steeper than a straight-line guess. Push q1 far above q2, too, and notice the force magnitude stays identical on both partners. The bigger charge does not win; Newton's third law hands each one an equal, opposite tug regardless of which you called q1.

The model is honest for two small spheres held well apart, and it strains when charged conductors sit almost touching, where induction reshuffles the charge. Pin down exact numbers with the Coulomb's law calculator, or tinker with neighbouring forces over at the full rack of physics playgrounds.

Where the ideal Coulomb's law breaks down

Everything here assumes the charge sits at a mathematical point. Real charge sits on the surface of a real conductor, and it moves. Push two like-charged spheres together and each drives the other's charge round to its far side, so the charge centres end up further apart than the sphere centres and the true repulsion is weaker than the readout claims; with opposite charges the charge crowds the near faces and the attraction is stronger. The point model holds while the gap exceeds about ten sphere radii, so the slider's minimum of 0.10 m gives the least trustworthy number in the lab.

The k on the panel, 8.99 × 10⁹ N·m²/C², is the vacuum value, and nothing here lets you change what sits between the charges. Fill the gap with a dielectric and every force divides by the relative permittivity: about 2.2 for polythene, roughly 80 for water. The default pair — two +5.0 µC charges 0.50 m apart, reading 0.899 N — would read about 11.2 mN underwater. That factor of eighty is why an ionic crystal welded solid in air falls apart into free ions in a glass of water.

The charge sliders promise more than physics delivers, too. Dry air breaks down near 3 MV/m, so an isolated sphere holds only Q = E·a²/k before it sprays its charge off as corona. A 5 cm sphere tops out around 0.83 µC, a sixth of the default setting, and the slider's full 10 µC needs a sphere 0.17 m in radius. Real demonstrations of this law work in nanocoulombs and millinewtons, not the newtons printed here.

Finally, this is electrostatics. Move a charge and the news of it takes 1.7 ns to cross the default 0.50 m gap, and moving charge also produces a magnetic force this lab never draws. Nor is the room otherwise empty: bring up a third charge, or a grounded metal bench, and both arrows change. Every real electrostatics problem is a superposition, and this is one term of it.

Where this is actually used

The strength of table salt. A sodium ion and a chloride ion in a salt crystal sit 0.282 nm apart, each carrying one elementary charge. Feed that into the expression the lab evaluates and the attraction is 2.90 nN: nothing in your hand, enormous per atom, and repeated over every neighbour in the lattice it is why sodium chloride does not melt until 801 °C. Distance does all the work — 0.10 m down to 0.282 nm is a factor of 3.5 × 10⁸, which the inverse square turns into 1.3 × 10¹⁷.

Finding the nucleus. Send a 5 MeV alpha particle (charge 2e) head-on at a gold nucleus (79e) and Coulomb's law says where it must stop: at 45 fm its kinetic energy is spent and it comes straight back. That was Rutherford's 1911 argument — alphas bouncing off something they never touched, so gold's positive charge had to be packed inside a radius under a thousandth of the atom's width.

The price of admission to fusion. Two deuterium nuclei must reach about 3 fm for the strong force to take over, and at that separation the same law gives 25.6 N between two single elementary charges — the weight of a 2.6 kg bag of sugar — with an energy barrier near 480 keV. That barrier, not the fuel, is why a fusion reactor has to run above a hundred million kelvin. It is the curve you walk down with the separation slider at fixed +5.0 µC charges: 56.2 mN at 2.00 m, 0.225 N at 1.00 m, 0.899 N at 0.50 m, 3.6 N at 0.25 m.