Physics
Electrostatics calculator: Coulomb, field and potential
Pick the relation and clear the unknown: force, charge, distance or field. Charges are entered in microcoulombs, the order of magnitude every exercise uses.
From force to field: why it pays to change viewpoint
Coulomb's law has the same shape as the law of gravitation: a product divided by the square of the distance. What differs is the constant, which is enormously larger, and the sign, which can be negative. Two one-coulomb charges a metre apart would repel with nine billion newtons — which is why exercise charges are measured in microcoulombs, and why ordinary matter is neutral to an extraordinary precision.
The step from force to field is the idea the rest of the course rests on. Instead of asking how charge A acts on charge B, we say that A fills space with a field E, and that B feels the force q·E wherever it sits. It is a restatement, not new physics, but it lets us describe sources that are not point charges and, later on, fields that travel on their own as waves.
The potential is energy per unit charge and falls off as 1/r, while the field falls off as 1/r². The difference is not a detail: the potential is a scalar and adds without regard to direction, whereas fields must be added as vectors. That is why, once a problem has more than two charges, starting from the potentials is almost always easier.
Common mistakes
- Mixing up the exponents: force and field go as 1/r², potential and energy as 1/r. Swapping them is wrong by a factor of r.
- Entering charges in coulombs when the exercise gives microcoulombs: 5 µC is 5 × 10⁻⁶ C, and typing 5 is wrong by twelve orders of magnitude. This calculator takes microcoulombs directly.
- Adding fields as if they were numbers: the field is a vector, and two equal and opposite fields cancel rather than double. The potential, by contrast, adds algebraically.
Frequently asked questions
What is the formula for Coulomb's law?
F = k·q₁·q₂/r², with k = 8.99 × 10⁹ N·m²/C². The force is attractive when the charges have opposite signs and repulsive when they have the same sign, and it acts along the line joining them.
What is the difference between electric field and electric potential?
The field is a force per unit charge, measured in N/C; the potential is an energy per unit charge, measured in volts. The field is a vector and goes as 1/r², the potential is a scalar and goes as 1/r.
Why can electrostatic potential energy be negative?
Because it is taken to be zero when the charges are infinitely far apart. Opposite charges attract, so work is needed to pull them apart: close together, their energy is below zero. Like charges instead have positive energy.
What is the constant k, and where does it come from?
k = 1/(4πε₀) ≈ 8.99 × 10⁹ N·m²/C², where ε₀ = 8.854 × 10⁻¹² F/m is the permittivity of free space. In a medium other than vacuum the force is reduced by the relative permittivity.
How this calculation works
Coulomb's law: F = k·q₁·q₂/r², with k = 1/(4πε₀) ≈ 8.99 × 10⁹ N·m²/C². Field of a point charge: E = k·q/r², pointing outwards for q > 0. Force on a charge in a field: F = q·E. Potential of a point charge: V = k·q/r, with V → 0 at infinity. Potential energy of a pair: U = k·q₁·q₂/r. Relations: E = V/r for a point charge, U = q·V, F = U/r. Elementary charge: e = 1.602 × 10⁻¹⁹ C.