Coulomb's Law states that the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. When an engineer or physicist is asked to state Coulomb's Law, this is the fundamental definition they must provide. Unlike Ohm's Law, which governs the flow of current through a resistance, Coulomb's Law governs the physical, mechanical forces exerted by stationary electrical charges on one another. It dictates everything from the microscopic attraction of dust to your monitor screen to the macroscopic clearance requirements on high-voltage power supplies.
The Core Formula and a Worked Numeric Example
To calculate the magnitude of the electrostatic force between two stationary point charges in a vacuum or air, we use the standard scalar form of the equation:
Where:
F = Electrostatic force in Newtons (N)
ke = Coulomb's constant, approximately 8.987 × 109 N·m2/C2 (sourced from NIST CODATA)
q1, q2 = Magnitude of the charges in Coulombs (C)
r = Distance between the centers of the charges in meters (m)
Let's run a worked numeric example to see how aggressively this inverse-square relationship scales. Imagine two isolated conductive spheres, each holding a static charge of 10 microcoulombs (10 µC, or 10 × 10-6 C). They are suspended in dry air exactly 50 millimeters (0.05 m) apart.
Step 1: Multiply the charges.
q1 * q2 = (10 × 10-6) * (10 × 10-6) = 100 × 10-12 C2 (or 1 × 10-10 C2)
Step 2: Square the distance.
r2 = (0.05)2 = 0.0025 m2
Step 3: Apply Coulomb's constant.
F = (8.987 × 109) * (1 × 10-10 / 0.0025)
F = 0.8987 / 0.0025
F = 359.48 Newtons
That is roughly 80.8 pounds of repulsive force generated by just 10 microcoulombs of charge. This massive mechanical force from a seemingly tiny amount of static charge is why electrostatic discharge (ESD) events can physically pit and damage silicon junctions.
How Medium and Permittivity Change the Force
The formula above assumes a vacuum. In the real world, charges are separated by insulating materials (dielectrics). The material between the charges resists the electric field, reducing the force. We account for this by dividing the vacuum force by the material's relative permittivity (dielectric constant, εr). According to HyperPhysics, the modified formula becomes F = Fvacuum / εr.
Here is how the 359.48 N force from our previous example drops depending on the insulating medium separating the charges:
| Dielectric Medium | Relative Permittivity (εr) | Resulting Force (N) | Practical Context |
|---|---|---|---|
| Vacuum | 1.0000 | 359.48 N | Spacecraft electronics, particle accelerators |
| Dry Air (1 atm) | 1.0006 | 359.26 N | Standard bench testing, overhead transmission |
| Transformer Oil | 2.2000 | 163.40 N | High-voltage switchgear cooling and insulation |
| FR-4 (Standard PCB) | 4.5000 | 79.88 N | Consumer electronics, 4-layer motherboards |
| Barium Titanate (Ceramic) | 1,200.00 | 0.30 N | Class II MLCC capacitors (X7R, Y5V dielectrics) |
Note: As the permittivity increases, the electrostatic force between the charges drops drastically. This is exactly why high-permittivity ceramics are used to build compact capacitors—they allow massive charge storage (high capacitance) while keeping the internal mechanical stresses between the plates manageable.
Where You Meet This in Practice
While Coulomb's Law is often treated as pure physics, it directly changes how we design real circuits and physical installations. It dictates physical clearances, component selection, and failure analysis in three specific areas:
1. High-Voltage PCB Clearance and Creepage
When routing 400V DC bus lines on a PCB, the electrostatic attraction between the copper traces and airborne conductive dust particles is governed by Coulomb's Law. Over time, the inverse-square force pulls metallic debris into the clearance gap. Once the debris bridges a fraction of the gap, the local electric field gradient spikes, leading to a cascading dielectric breakdown and a dead short. Designers must increase physical clearance distances not just to prevent air ionization (Paschen's Law), but to reduce the Coulomb force pulling in environmental contaminants.
2. Capacitor Microphonics and Plate Attraction
In multi-layer ceramic capacitors (MLCCs), the dielectric layers are incredibly thin (often under 1 micron). When a high AC ripple voltage is applied, the charges on the opposing internal plates constantly attract each other. The mechanical force pulling the plates together physically deforms the ceramic body. In high-permittivity materials like Y5V, this electrostatic attraction couples with the piezoelectric effect, causing the capacitor to vibrate at the ripple frequency. This is the root cause of audible "coil whine" or "singing capacitors" on modern graphics cards and switching power supplies.
3. ESD Snap-Over and Arcing
When you walk across a carpet and reach for a grounded doorknob, you are carrying a static charge. As your finger approaches the knob, the distance (r) decreases. Because the force scales with 1/r2, the electrostatic pull on the electrons in your skin spikes exponentially in the final few millimeters. This massive, sudden force gradient rips electrons from the air molecules, ionizing the gap and creating a conductive plasma channel. The "snap" you feel is the physical manifestation of the inverse-square law reaching a critical threshold.
Common Confusions: Electrostatics vs. Electrodynamics
The most frequent mistake made by junior engineers and trade students is confusing Coulomb's Law with Ampere's Force Law. They sound similar and both describe forces in electrical systems, but they govern entirely different physical phenomena.
Coulomb's Law applies to stationary charges (Electrostatics). It explains why two statically charged balloons repel each other, or why dust sticks to a screen. It does not require a closed circuit or current flow.
Ampere's Force Law applies to moving charges (Electrodynamics). It describes the magnetic force between two current-carrying wires. When a 50kA short circuit occurs in a commercial switchgear panel, the massive magnetic fields generated by the moving electrons cause the copper busbars to physically bend, warp, or violently repel each other. That is Ampere's Law in action, not Coulomb's.
If you are calculating the physical stress on a busbar during a fault condition, or sizing the bracing for a transformer winding, you must use electromagnetic force equations (Lorentz force / Ampere's Law). If you are calculating the attraction of a charged toner particle to a drum, or the force required to trigger an electrostatic MEMS relay, you use Coulomb's Law.
Frequently Asked Questions
Does Coulomb's Law apply to alternating current (AC) circuits?
No. In an AC circuit, the charges are in constant motion, generating time-varying magnetic fields. The interactions are governed by Maxwell's equations and electrodynamics. Coulomb's Law is strictly an electrostatic approximation for charges at rest, or moving at speeds negligible compared to the speed of light.
How does the law relate to the unit "Coulomb"?
Ironically, the unit of charge (the Coulomb) is not defined by Coulomb's Law in modern metrology. Since the 2019 SI redefinition, the Coulomb is defined by fixing the elementary charge of an electron to exactly 1.602176634 × 10-19 C. Coulomb's Law simply uses this predefined unit to calculate the resulting mechanical force.
Why does the force drop so fast in FR-4 compared to air?
FR-4 is a woven glass-epoxy composite with a relative permittivity of roughly 4.5. The polar molecules within the epoxy align themselves against the applied electric field, creating an internal "back-field" that partially cancels the original field. This shielding effect reduces the net electrostatic force between the embedded copper charges by a factor of 4.5 compared to a vacuum.
