7.19
N
7.19
N
1
3,595,000
N/C
0.3595
J
179,750
V
7.19
N
7.19
N
1
3,595,000
N/C
0.3595
J
179,750
V
Coulomb's Law Calculator computes the electrostatic force between two point charges separated by a distance. Formulated by French physicist Charles-Augustin de Coulomb in 1785, this fundamental law of electrostatics describes how charged particles interact. The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This inverse-square relationship mirrors Newton's law of gravitation, though electrostatic forces can be either attractive or repulsive depending on the signs of the charges. Coulomb's Law is foundational to understanding electric fields, capacitor design, molecular bonding, and semiconductor physics. The proportionality constant $$k = 8.9875 \times 10^9 \, \text{N m}^2/\text{C}^2$$ is related to the permittivity of free space by $$k = \frac{1}{4\pi\varepsilon_0}$$. This calculator determines the magnitude and direction (attractive or repulsive) of the force, along with the electric field created by one charge at the location of the other.
The calculator applies Coulomb's Law:
$$F = k \frac{|q_1 q_2|}{r^2}$$
where:
The force direction depends on the charge signs: like charges (both positive or both negative) repel each other, while opposite charges attract. The electric field at the location of q₂ due to q₁ is calculated as $$E = k\frac{|q_1|}{r^2}$$, which represents the force per unit charge. Coulomb's Law applies exactly to point charges and spherically symmetric charge distributions. For extended charge distributions, the principle of superposition allows summing contributions from infinitesimal charge elements. In a medium other than vacuum, the force is reduced by the dielectric constant κ of the medium: $$F = \frac{kq_1q_2}{\kappa r^2}$$.
The result gives the magnitude of the electrostatic force and whether it is attractive or repulsive. A positive product of charges means repulsion; a negative product means attraction. Note that 1 coulomb is an enormous charge — typical laboratory charges are in microcoulombs (μC = 10⁻⁶ C) or nanocoulombs (nC = 10⁻⁹ C). Electrostatic forces are incredibly strong compared to gravitational forces: the electrostatic repulsion between two protons is about 10³⁶ times stronger than their gravitational attraction. The electric field output shows the field strength at the second charge's position, useful for understanding the influence of q₁ independent of the test charge q₂.
Inputs
Results
Two positive charges of 1 μC and 2 μC separated by 5 cm experience a repulsive force of approximately 7.19 N. This demonstrates that even microcoulomb charges at centimeter separations produce forces comparable to everyday gravitational forces.
Inputs
Results
A +3 μC charge and a −5 μC charge separated by 10 cm attract each other with a force of about 13.48 N. The negative product of charges confirms the attractive nature of the interaction.
Coulomb's Law states that the electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. The law is expressed as F = kq₁q₂/r², where k ≈ 8.9875 × 10⁹ N·m²/C². Like charges repel and opposite charges attract.
Coulomb's constant k = 8.9875 × 10⁹ N·m²/C² is related to the permittivity of free space ε₀ by k = 1/(4πε₀), where ε₀ = 8.854 × 10⁻¹² F/m. In a dielectric medium with relative permittivity κ, the effective constant becomes k/κ, reducing the force between charges.
Coulomb's Law in its simple form applies to point charges or spherically symmetric charge distributions (by treating them as point charges at their centers). For arbitrary charge distributions, you must integrate the contributions from all infinitesimal charge elements using the principle of superposition. Gauss's Law provides a more convenient approach for highly symmetric distributions.
Electrostatic forces are vastly stronger than gravitational forces. For two protons, the electrostatic repulsion is approximately 10³⁶ times greater than their gravitational attraction. However, gravity dominates at large scales because bulk matter is electrically neutral — positive and negative charges cancel — while mass always adds constructively.
Charges should be entered in coulombs (C). Since 1 coulomb is an extremely large charge, practical values are typically in microcoulombs (1 μC = 10⁻⁶ C), nanocoulombs (1 nC = 10⁻⁹ C), or picocoulombs (1 pC = 10⁻¹² C). The elementary charge (charge of one proton) is e = 1.602 × 10⁻¹⁹ C.
Coulomb's Law strictly applies to stationary (static) charges. For moving charges, magnetic forces also arise, described by the Lorentz force law: F = q(E + v × B). The complete interaction between moving charges requires the full framework of electrodynamics, including retardation effects. However, Coulomb's Law remains a good approximation when charge velocities are much less than the speed of light.
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