Coulomb’s law and electric field calculator
Force between two charges, field created by one charge and force on a test charge, with the attractive or repulsive nature named.
Result
0.898 755 N
- Calculation
- F = k·|q₁q₂|/r² = 8.98755 × 10⁹ × |1 × 10⁻⁶ × 1 × 10⁻⁶| / 0.1² = 0.898 755 N
- Nature
- repulsive, the charges have the same sign
- That is, in elementary charges
- 6.24151 × 10¹²
- Coulomb constant
- 8.98755 × 10⁹ N·m²/C²
Notes (2)
The two forces are equal and opposite. At twice the distance, a quarter remains.
The force is 0.898 755 N; it is repulsive, the charges have the same sign.
Calculation, assumptions and sources
OverviewCoulomb’s law in its two forms: the force between two charges, F = k·q₁q₂/r², and the field created by one charge, E = k·q/r², with the force on a test charge.
Coulomb’s law in its two forms: the force between two charges, F = k·q₁q₂/r², and the field created by one charge, E = k·q/r², with the force on a test charge. The constant k is computed from the CODATA vacuum permittivity; the nature of the force, attractive or repulsive, is named in words.
Method & formulasF = k · |q₁ q₂| / r²
The force falls as the square of the distance, like gravitation. The constant k is computed from the vacuum permittivity ε₀.
- q
- electric charge, in coulombs. The sign is part of the charge.
- Elementary charge
- e = 1.602 176 634 × 10⁻¹⁹ C, exact since the 2019 SI: the charge of the proton, the opposite of the electron’s.
- E
- electric field, in volts per metre, a unit equal to the newton per coulomb.
- ε₀
- vacuum permittivity, 8.854 × 10⁻¹² F/m (CODATA 2018).
Validity domainThe law holds for point charges, or spherically symmetric ones seen from outside, at rest and in vacuum.
The law holds for point charges, or spherically symmetric ones seen from outside, at rest and in vacuum. Inside a material the relative permittivity divides the force; for fast-moving charges, magnetism adds on. At the atomic scale, quantum mechanics governs bound states: the law gives the order of magnitude of the hydrogen atom, not its energy levels. At zero distance, the law diverges.
Reading the resultThe sign of the charges sets the nature of the force, attractive or repulsive, not its magnitude.
The sign of the charges sets the nature of the force, attractive or repulsive, not its magnitude. The field describes the force a charge placed at that point would feel. The law has the same 1/r² form as gravitation; between a proton and an electron, the electric force is 10³⁹ times larger.