To summarize Coulomb's law in a sentence: the electrostatic force between two point charges is directly proportional to the product of their charge magnitudes and inversely proportional to the square of the distance separating them. While this sounds like abstract textbook physics, it is the foundational rule governing everything from why dust aggressively sticks to your freshly soldered PCBs, to the exact air gap required to prevent a 600V DC solar string from arcing across your combiner box.
The Formula and a Worked Numeric Example
Coulomb's law quantifies the invisible push or pull between stationary electrical charges. The scalar form of the equation is:
F = ke (|q1 q2|) / r2
- F = Electrostatic force (Newtons, N)
- ke = Coulomb's constant (approximately 8.987 × 109 N·m²/C² in a vacuum/air)
- q1, q2 = The signed magnitudes of the two charges (Coulombs, C)
- r = Distance between the centers of the charges (meters, m)
Real-World Numeric Example: The Workbench Static Snap
Imagine you are working on a dry winter day. You slide out of a nylon chair, building up a triboelectric static charge on your body. You reach toward an ungrounded, metal-shielded Arduino enclosure sitting on your ESD mat. Let's model your fingertip and the enclosure as two point charges.
- Charge on fingertip (q1): +2 μC (2 × 10-6 C)
- Induced charge on enclosure (q2): -2 μC (-2 × 10-6 C)
- Distance (r): 2 cm (0.02 m) just before the spark jumps
Plugging these into the formula:
F = (8.987 × 109) × [ (2 × 10-6) × (-2 × 10-6) ] / (0.02)2
F = (8.987 × 109) × [ -4 × 10-12 ] / 0.0004
F = (8.987 × 109) × (-1 × 10-8)
That is a massive amount of mechanical force concentrated on a microscopic point. This intense localized attraction is exactly what accelerates free electrons across the air gap, ionizing the air and creating the visible, component-killing spark we call Electrostatic Discharge (ESD). According to the ESD Association, a human-body-model spark of just 100V can permanently destroy the gate oxide of a sensitive MOSFET, long before you even feel the shock.
Where You Meet Coulomb's Law in Practice
You might think electrostatics only matters in a physics lab, but Coulomb's law dictates physical constraints in real circuits, PCB layouts, and high-voltage installations.
1. PCB Clearance and Creepage Distances
When routing high-voltage traces (like the primary side of an offline SMPS or a 400V DC bus), the repulsive and attractive forces between adjacent conductors create an electric field. If the voltage gradient exceeds the dielectric breakdown strength of air (roughly 3 kV/mm at standard temperature and pressure), Coulombic forces rip electrons from air molecules, causing an arc. Standards like IPC-2221 mandate specific physical spacing (clearance through air, and creepage across the board surface) to ensure the electrostatic force never reaches the threshold required to ionize the gap.
2. Multilayer Ceramic Capacitor (MLCC) Mechanical Stress
Inside an MLCC, dozens of microscopic metal plates are separated by thin ceramic dielectrics. When a DC voltage is applied, opposite charges accumulate on adjacent plates. Coulomb's law dictates that these plates physically attract one another. In high-capacitance, high-voltage MLCCs, this electrostatic attraction causes the ceramic dielectric to physically compress—a phenomenon known as piezoelectric deformation or DC bias acoustic noise. If the Coulombic force exceeds the mechanical tensile strength of the ceramic, the capacitor cracks internally, resulting in a dead short.
3. High-Voltage Insulator Design
In solar combiner boxes or mains service entrances, insulators must withstand not just the voltage, but the electrostatic forces attempting to pull conductive dust and moisture across the gap. The inverse-square nature of the law means that increasing the physical air gap is vastly more effective at reducing electrostatic stress than simply adding more insulating material.
What People Commonly Confuse It With
Because electrical theory involves several foundational laws named after 18th and 19th-century physicists, builders frequently mix them up. Here is how to keep them straight on the bench.
| Law | Domain | What It Calculates | Key Variable |
|---|---|---|---|
| Coulomb's Law | Electrostatics | Force between stationary charges through space | Distance (r2) |
| Ohm's Law | Electrodynamics (Circuits) | Current flow through a resistive medium | Resistance (R) |
| Ampere's Force Law | Magnetostatics | Force between two current-carrying wires | Current (I1, I2) |
| Faraday's Law | Electromagnetic Induction | Voltage induced by a changing magnetic field | Time (dt) |
The short version: Ohm's law tells you how much current will flow through your 10 AWG wire. Ampere's law tells you how much those two parallel wires will physically push apart during a 10,000A short-circuit fault. Coulomb's law tells you how much force is pulling static dust onto the board before you even power it up.
Frequently Asked Questions
How do you summarize Coulomb's law in a sentence for a physics test?
The most universally accepted academic summary is: "The magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them." This perfectly captures the direct and inverse relationships required for full marks.
Does Coulomb's law apply to AC circuits?
Strictly speaking, Coulomb's law applies only to electrostatics (charges at rest). In an AC circuit, charges are constantly accelerating and decelerating, which generates changing magnetic fields and electromagnetic radiation. However, at low frequencies (like 50/60Hz mains power), the charges move slowly enough that the "electrostatic approximation" holds true for calculating instantaneous capacitive coupling and electric field gradients between adjacent traces or busbars.
What is the difference between a Coulomb and Coulomb's Law?
A Coulomb (C) is the standard SI unit of electrical charge, defined as the amount of charge transported by a constant current of one ampere in one second (1 C = 1 A × 1 s). Coulomb's Law is the physical equation that describes how those charges interact with one another mechanically across a distance. One is a unit of measurement; the other is a rule of physical behavior.
How does the dielectric material change Coulomb's force?
The constant ke in the formula assumes a vacuum. If you place a dielectric material (like FR4 fiberglass, Teflon, or transformer oil) between the two charges, the electrostatic force is reduced. This is calculated by dividing Coulomb's constant by the relative permittivity (dielectric constant, εr) of the material. For example, placing a piece of FR4 (εr ≈ 4.5) between two charged plates reduces the attractive force between them by a factor of 4.5 compared to air. This principle is why high-voltage switchgear uses SF6 gas or specialized oils to suppress arcing.
