18.1 Static Electricity and Charge: Conservation of Charge

Electric Charge and Interactions

Electric charge is a fundamental property of matter that determines how objects interact electromagnetically. Positive and negative charges attract each other, while like charges repel. This principle governs everything from the static shock you get touching a doorknob to the behavior of subatomic particles.

Conservation of charge is one of the most important laws in physics: the total charge in a closed system always remains constant. Charge is never created or destroyed; it only moves from one place to another. This concept is central to understanding static electricity, electric currents, and how charges transfer between objects.

Electric Charge Interactions

All matter contains electric charge, and there are exactly two types: positive (carried by protons) and negative (carried by electrons). The basic interaction rules are simple:

• Like charges repel each other (positive repels positive, negative repels negative)
• Opposite charges attract each other (positive attracts negative)

Protons and electrons carry the same magnitude of charge but with opposite signs. The elementary charge has a value of $e = 1.6 \times 10^{-19}$ coulombs.

A neutral object has equal numbers of protons and electrons, so the charges cancel out and there's no net charge. A charged object has an imbalance:

• More protons than electrons → net positive charge
• More electrons than protons → net negative charge

Note that in most everyday situations, it's the electrons that move, not the protons. Protons are locked inside atomic nuclei. So when an object becomes positively charged, it has lost electrons rather than gained protons.

Coulomb's law describes the force between two charged objects:

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

where $F$ is the electric force, $k$ is Coulomb's constant ($8.99 \times 10^9 \, \text{N·m}^2/\text{C}^2$), $q_1$ and $q_2$ are the two charges, and $r$ is the distance between them.

Two things to notice here:

• The force is directly proportional to the product of the charges. Double one charge, and the force doubles.
• The force is inversely proportional to the square of the distance. Double the distance, and the force drops to one-quarter.

Examples of Static Electricity

Static electricity happens when charge builds up on an object's surface, usually through friction (called triboelectric charging). In every case below, electrons transfer from one material to another.

• Balloon on hair: Rubbing a balloon on your hair transfers electrons from the hair to the balloon. The balloon becomes negatively charged, and your hair becomes positively charged, which is why individual strands repel each other and stand up.
• Carpet shock: Walking across carpet in socks builds up charge on your body through friction. When you touch a metal doorknob, that charge rapidly discharges, producing a small spark.
• Static cling: Pulling off a sweater creates friction between the fabric and your body or other clothing. The transferred charges cause garments to stick together.
• Combing hair: A plastic comb run through hair picks up electrons from the hair. The now-negatively-charged comb can attract small neutral objects like bits of paper.
• Glass rod and silk: Rubbing a glass rod with silk transfers electrons from the glass to the silk. The glass rod ends up positively charged, and the silk becomes negatively charged. The rod can then attract small pieces of paper.

In every one of these examples, the total charge of the system (both objects combined) stays the same. That's conservation of charge in action.

Conservation of Charge Law

The law of conservation of charge states that the net electric charge in an isolated system remains constant. Charge cannot be created or destroyed; it can only be transferred from one object to another or redistributed within a system.

Here's what this looks like in practice:

1. When you rub a balloon on your hair, the balloon gains a certain amount of negative charge. Your hair loses that exact same amount of negative charge (becoming positive). The total charge of the balloon-plus-hair system hasn't changed.
2. In a chemical reaction inside a battery, charges are transferred between atoms and molecules, but the total charge before and after the reaction is identical.
3. Even in nuclear reactions and particle physics, total charge is always conserved.

This law applies universally across physics and chemistry. It's not just a rule for static electricity; it holds in every known physical process.

Electric Fields and Related Concepts

• Electric field: A region around a charged object where other charges experience a force. Electric fields are represented by field lines that point in the direction a positive test charge would be pushed. Closer field lines mean a stronger field.
• Electric potential: The potential energy per unit charge at a point in an electric field, measured in volts (V). It tells you how much work is needed to move a charge to that point.
• Polarization: When an external electric field causes the positive and negative charges within a neutral material to shift slightly in opposite directions. This is why a charged balloon can stick to a neutral wall: the balloon's charge polarizes the wall's surface, creating a net attraction.
• Insulators: Materials like rubber, glass, and plastic that resist the flow of electric charge. They're important for controlling where charge can and can't go. (This is why static charge stays put on a balloon instead of spreading out immediately.)