Electric Force Calculator
Calculate electrostatic force between two point charges using Coulomb’s law: F = k|q₁q₂|/r², where k = 8.9875517923 × 10⁹ N·m²/C². Supports unit conversions for charge, distance, and force.
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What is Electric Force?
Electric force is the fundamental interaction between charged particles that causes attraction (opposite charges) or repulsion (like charges). It is one of the four fundamental forces of nature and is described by Coulomb’s law:
F = k|q₁q₂| / r²
Where F is force in newtons (N), k = 8.9875517923 × 10⁹ N·m²/C² is Coulomb’s constant, q₁ and q₂ are charges in coulombs (C), and r is the separation distance in meters (m). The direction of force is along the line connecting the charges.
Common Electrostatic Force Values
| Scenario | Force (N) |
|---|---|
| Electron–proton in hydrogen atom | 8.200e-8 |
| Two 1 C charges 1 km apart | 8.988e+3 |
| Two electrons 1 cm apart | 2.300e-24 |
| Lightning bolt (typical) | 1.000e+8 |
| Static shock (two charged bodies, 1 mm) | 1.000e-1 |
| Two protons in atomic nucleus (1 fm) | 2.300e+2 |
| Van de Graaff generator discharge | 1.000e+0 |
| Charged balloon on hair (3 cm, 1 μC) | 1.000e+1 |
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Authoritative References
Frequently Asked Questions
What is electric force?
Electric force is the attractive or repulsive interaction between charged particles. It is described by Coulomb’s law: F = k|q₁q₂|/r², where k = 8.9875517923 × 10⁹ N·m²/C². Like charges repel, opposite charges attract.
What is Coulomb’s law?
Coulomb’s law quantifies the electric force between two stationary point charges. The force is proportional to the product of the charges and inversely proportional to the square of the distance between them. It was published by Charles-Augustin de Coulomb in 1785 using a torsion balance.
What is the value of Coulomb’s constant k?
Coulomb’s constant k = 8.9875517923 × 10⁹ N·m²/C². It is related to the permittivity of free space by k = 1/(4πε₀), where ε₀ = 8.854187817 × 10⁻¹² F/m.
How does distance affect electric force?
The electric force follows an inverse-square law: F ∝ 1/r². Doubling the distance reduces the force to one-quarter of its original value. Halving the distance quadruples the force. This makes electric force highly sensitive to separation distance.
What is the difference between electric force and gravitational force?
Electric force can be either attractive or repulsive, while gravity is only attractive. Electric force is about 10³⁹ times stronger than gravity for elementary particles. However, gravity dominates at large scales because matter is electrically neutral overall.
What is an elementary charge?
The elementary charge e = 1.602176634 × 10⁻¹⁹ C is the fundamental unit of electric charge. Protons have charge +e, electrons have charge –e, and all free charges are integer multiples of e. Quarks have fractional charges but are never observed in isolation.
What is the force between two electrons?
Two electrons repel each other with an electric force proportional to 1/r². At 1 m apart, the repulsive force is F = ke²/r² = 2.3 × 10⁻²⁸ N. At 1 cm apart, it is 2.3 × 10⁻²⁴ N, which is extremely small but measurable in sensitive experiments.
What is the force between a proton and an electron?
A proton and electron attract each other. In a hydrogen atom at the Bohr radius (5.29 × 10⁻¹¹ m), the electric force is F = ke²/r² = 8.2 × 10⁻⁸ N. This centripetal force keeps the electron in orbit around the proton.
How is Coulomb’s law used in chemistry?
Coulomb’s law explains ionic bonding (attraction between positive and negative ions), lattice energy in crystals, the periodic trends of ionization energy and electron affinity, and the forces between atoms in molecules. It is fundamental to understanding chemical bonding.
What is the permittivity of free space?
The permittivity of free space ε₀ = 8.854187817 × 10⁻¹² F/m describes how an electric field penetrates vacuum. It appears in Coulomb’s law through k = 1/(4πε₀). Materials with higher permittivity reduce the force between charges.
What happens when charges are in a medium?
In a dielectric medium, the electric force is reduced by the dielectric constant (relative permittivity εᵣ). The effective force becomes F = k|q₁q₂|/(εᵣr²). Water (εᵣ ≈ 80) reduces the force by a factor of 80 compared to vacuum.
How strong is the electric force in a lightning bolt?
A typical lightning bolt transfers about 15–20 C of charge between clouds and ground. The electric force during a lightning strike can exceed 10⁸ N, powerful enough to ionize air, create plasma channels, and deliver enormous destructive energy.
What is the superposition principle for electric forces?
The superposition principle states that the total electric force on a charge is the vector sum of forces from all other charges. Each pair interaction follows Coulomb’s law independently, and the net force is found by adding these vectors component by component.
What is a newton of force in practical terms?
One newton is roughly the weight of a 100 g apple on Earth. A micronewton (μN) is the force between two 1 C charges separated by about 95 km. A piconewton (pN) is typical of molecular-scale forces in biology and nanotechnology.
How does Coulomb’s law relate to electric fields?
Coulomb’s law can be rewritten in terms of electric field: F = qE, where E = kQ/r² is the electric field created by charge Q. This field viewpoint is fundamental to electromagnetism and describes how charges interact across space.
What is an electric dipole?
An electric dipole consists of two equal and opposite charges separated by a small distance. The dipole moment p = qd. Dipoles experience torque in electric fields and produce fields that fall off as 1/r³, faster than single charges.
How do charged balloons demonstrate electric force?
Rubbing a balloon on hair transfers electrons, giving it a negative charge (several μC). The balloon can then stick to a wall by inducing opposite charges in the wall. The attractive force at 1–3 mm distance is strong enough to hold the balloon’s weight.
What is the Van de Graaff generator?
A Van de Graaff generator uses a moving belt to accumulate electrostatic charge on a metal dome, reaching voltages of hundreds of kilovolts. It demonstrates electric force by making hair stand up (like charges repel) and producing visible sparks.
How is electric force involved in chemical bonds?
Ionic bonds form when electrons transfer between atoms, creating ions that attract via Coulomb’s law. Covalent bonds involve sharing electrons, where the attractive force between nuclei and shared electrons balances the repulsive forces between nuclei.
What is the Millikan oil drop experiment?
The Millikan oil drop experiment (1909) measured the elementary charge by balancing the electric force on charged oil drops against gravity. Millikan found that all charges were integer multiples of e = 1.592 × 10⁻¹⁹ C, close to the modern value.
What is the force between charges in a vacuum vs. air?
Air has a relative permittivity of about 1.0006, so the force in air is nearly identical to vacuum. The difference is only about 0.06%. For most practical purposes, Coulomb’s law in air is equivalent to vacuum.
How does Coulomb’s law apply to continuous charge distributions?
For continuous distributions, the force is found by integration: divide the distribution into infinitesimal charge elements dq, apply Coulomb’s law for each element, and integrate over the entire distribution. Gauss’s law provides a simpler method for symmetric distributions.
What is the relationship between Coulomb’s law and Gauss’s law?
Gauss’s law is a more general formulation of electrostatics. For a point charge, Gauss’s law yields the same 1/r² field as Coulomb’s law. Coulomb’s law is a special case of Gauss’s law for static point charges, but Gauss’s law extends to dynamic fields via Maxwell’s equations.
Can Coulomb’s law be used for moving charges?
Coulomb’s law is strictly valid only for stationary (or slowly moving) point charges. For moving charges, magnetic forces and relativistic effects must be included. The full Lorentz force law F = q(E + v × B) describes the complete electromagnetic interaction.
What is electrostatic induction?
Electrostatic induction is the redistribution of charge in a conductor due to the presence of nearby charges. The electric force from the external charge attracts opposite charges and repels like charges, creating induced charges without direct contact.
How is Coulomb’s law used in particle physics?
Coulomb’s law describes the electromagnetic interaction between charged particles. In particle accelerators, it governs beam–beam interactions. In atoms, it determines electron binding energies. At very short distances, quantum electrodynamics (QED) provides more accurate descriptions.
What is the strong force vs. electric force in the nucleus?
Inside the nucleus, protons repel each other via the electric force (Coulomb repulsion). The strong nuclear force, which is about 100 times stronger than electric force at short ranges, overcomes this repulsion and binds protons and neutrons together.
What is a pound-force (lbf)?
One pound-force (lbf) is the force exerted by gravity on one pound of mass at Earth’s surface. 1 lbf = 4.448222 N. It is commonly used in the United States for engineering and everyday measurements of force.
How do electrostatic precipitators use electric force?
Electrostatic precipitators remove particulate matter from exhaust gases. Charged particles are attracted to oppositely charged collector plates by electric force. This technology is widely used in power plants and industrial facilities to reduce air pollution.
What is the Casimir effect?
The Casimir effect is a quantum phenomenon where two uncharged conducting plates attract each other due to vacuum fluctuations of the electromagnetic field. Although not directly Coulomb’s law, it is an important quantum electrodynamic force at nanometer scales.