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. It explains why a balloon can stick to a wall, why clothes crackle in a dryer, and why you may feel a spark after walking on carpet.

In most everyday solids, the useful model is that electrons move from one material to another. If an object gains electrons, it becomes negatively charged. If it loses electrons, it becomes positively charged.

How Static Electricity Builds Up

Contact And Separation

Many static-electricity examples start when two materials touch and then separate. During that process, some electrons can transfer from one surface to the other. Rubbing can make the effect stronger because it increases contact, but it does not create charge from nothing.

Conduction

If a charged object touches another object, charge can move by direct contact. Afterward, both objects may share charge, though the result depends on the materials and on whether either object is grounded.

Induction

A nearby charged object can also rearrange charges inside another object without touching it. By itself, induction usually causes charge separation, not a permanent net charge. If grounding is added under the right conditions, induction can leave the object with a net charge.

Coulomb's Law For Static Charge

Static electricity is part of electrostatics, which studies charges at rest. The main force law is Coulomb's law.

For two point charges in vacuum,

$$F = k \frac{|q_1 q_2|}{r^2}$$

where $F$ is the force magnitude, $q_1$ and $q_2$ are the charges, $r$ is the separation distance, and $k \approx 8.99 \times 10^9\ \mathrm{N \cdot m^2/C^2}$.

This formula gives the size of the force. The signs of the charges tell you the direction:

• like charges repel
• unlike charges attract

Coulomb's law applies directly when the charges can be treated as point charges. For real objects such as a balloon or a wall, charge is spread over a surface, so the exact force is more complicated. Still, the law gives the key pattern: larger charges produce stronger forces, and doubling the distance makes the force four times smaller.

Worked Example: Force Between Two Charges

Suppose two small charged spheres have charges

• $q_1 = 40\ \mathrm{nC} = 40 \times 10^{-9}\ \mathrm{C}$
• $q_2 = -20\ \mathrm{nC} = -20 \times 10^{-9}\ \mathrm{C}$
• $r = 5.0\ \mathrm{cm} = 0.050\ \mathrm{m}$

Find the force magnitude and decide whether it is attractive or repulsive.

Start with Coulomb's law:

$$F = k \frac{|q_1 q_2|}{r^2}$$

Substitute the values:

$$F = (8.99 \times 10^9)\frac{|(40 \times 10^{-9})(-20 \times 10^{-9})|}{(0.050)^2}$$

Multiply the charges:

$$|q_1 q_2| = 8.0 \times 10^\{-16\}\ \mathrm\{C^2\}$$

Square the distance:

$$r^2 = 2.5 \times 10^{-3}\ \mathrm{m^2}$$

Now compute the force:

$$F = (8.99 \times 10^9)\frac{8.0 \times 10^{-16}}{2.5 \times 10^{-3}} \approx 2.9 \times 10^{-3}\ \mathrm{N}$$

So the force magnitude is about $2.9\ \mathrm{mN}$. Because the charges have opposite signs, the force is attractive.

The main takeaway is the inverse-square pattern. If the distance doubled while the charges stayed the same, the force would become one-fourth as large.

Why A Charged Balloon Sticks To A Wall

When you rub a balloon on hair or fabric, charge can transfer to the balloon. If you bring that charged balloon near a wall, charges inside the wall shift slightly. This polarization can create a net attraction even if the wall as a whole stays electrically neutral.

This example shows why everyday static electricity is often about both charge transfer and charge rearrangement, not just two isolated point charges.

Common Mistakes In Static Electricity

• Saying rubbing creates charge from nothing. It usually helps transfer charge between materials.
• Forgetting that electrons are typically the mobile charges in everyday solids.
• Using Coulomb's law as if every real object were a point charge.
• Ignoring units when converting nanocoulombs or centimeters to SI units.
• Assuming induction always leaves a permanent net charge. That usually requires grounding as well.

Where Static Electricity Is Used

Static electricity matters in photocopiers, laser printers, electrostatic precipitators, powder coating, and some industrial separation processes. It also matters in electronics handling, where an electrostatic discharge can damage sensitive components even when the spark is too small to notice.

Humidity also matters. In dry air, charge tends to remain on surfaces longer, so static effects are often easier to notice.

Try A Similar Coulomb's Law Problem

Keep the same charges from the worked example, but change the distance from $0.050\ \mathrm{m}$ to $0.10\ \mathrm{m}$. Solve for the new force before using a calculator, then check whether the inverse-square result matches your intuition.