Static Electricity — Charging, Coulomb's Law & Examples

Static electricity is electric charge that builds up on an object instead of flowing as a steady current, and the quantitative core of the topic is a single force law. Once you know two charges and how far apart they are, Coulomb's law gives the strength of the force between them, while the signs tell you its direction.

Coulomb's Law And Its Symbols

For two point charges in vacuum,

where $F$ is the force magnitude, $q_1$ and $q_2$ are the charges, $r$ is the separation distance, and $k \approx 8.99 \times 10^9\ \mathrm{N \cdot m^2/C^2}$. The formula gives only the size of the force; the signs of the charges set the direction, with like charges repelling and unlike charges attracting.

Why The Force Behaves This Way

The useful everyday model is that electrons move between materials: an object that gains electrons becomes negative, and one that loses electrons becomes positive. That charge can arrive several ways. In contact and separation, two surfaces touch and some electrons transfer; rubbing strengthens the effect by increasing contact but does not create charge from nothing. In conduction, a charged object touching another lets charge move by direct contact. In induction, a nearby charged object rearranges charges inside another without touching, which by itself causes separation rather than a net charge unless grounding is added. The $1/r^2$ dependence is the part that surprises students: because the force falls with the square of distance, doubling the separation makes the force four times smaller. That inverse-square pattern is the single most important behaviour to internalize.

Worked Example: Force Between Two Charges

Two small charged spheres carry $q_1 = 40\ \mathrm{nC} = 40 \times 10^{-9}\ \mathrm{C}$ and $q_2 = -20\ \mathrm{nC} = -20 \times 10^{-9}\ \mathrm{C}$, separated by $r = 5.0\ \mathrm{cm} = 0.050\ \mathrm{m}$. Find the magnitude and whether it is attractive or repulsive.

Substituting into Coulomb's law,

The charge product and the squared distance are

so

The force magnitude is about $2.9\ \mathrm{mN}$, and because the charges have opposite signs, it is attractive.

Try It Yourself

Keep the same two charges but change the separation from $0.050\ \mathrm{m}$ to $0.10\ \mathrm{m}$, doubling the distance. Predict the new force before reaching for a calculator: by the inverse-square rule the force should drop to one-fourth, so about $0.7\ \mathrm{mN}$. Working it out and checking against that prediction is the fastest way to confirm you trust the $1/r^2$ behaviour rather than just the formula.

Pitfalls In Static-Electricity Calculations

• Ignoring unit conversions. Nanocoulombs and centimetres must become coulombs and metres before substituting, or the powers of ten go wrong.
• Treating every object as a point charge. Coulomb's law applies directly to point charges; for a balloon or wall, charge spreads over a surface and the exact force is more complicated, though the larger-charge and inverse-square trends still hold.
• Saying rubbing creates charge. It transfers charge between materials.
• Forgetting electrons are the mobile charges in everyday solids.
• Assuming induction leaves a permanent net charge. That usually requires grounding as well.

For a real case, a balloon rubbed on hair gains charge, and near a wall it shifts the wall's charges slightly; this polarization can attract the balloon even though the wall stays neutral overall, which is why everyday static is often about both transfer and rearrangement, not two isolated point charges.

Where Static Electricity Is Used

The same physics drives photocopiers, laser printers, electrostatic precipitators, powder coating, and industrial separation. It also governs electronics handling, where an electrostatic discharge can damage sensitive components even when the spark is too small to feel. Humidity matters too: in dry air, charge lingers on surfaces longer, so static effects are easier to notice.