Topic 8.1 Notes – Electric Charge and Electric Force

1. What Electric Charge Is

Charge as a fundamental property

Electric charge is an intrinsic property of matter, just like mass. It isn’t something objects “get” from motion or contact. It’s built in.

• It is a scalar quantity → it has magnitude and sign (+ or −), but no direction.
• Measured in coulombs (C).
• The sign matters because it determines how objects interact.

Elementary charge and subatomic particles

The smallest unit of charge we observe is the elementary charge:

$$e = 1.602 \times 10^{-19}\ \text{C}$$

• Electron → $-e$
• Proton → $+e$
• Neutron → 0

All observable charge comes in integer multiples of $e$. This is the quantization of charge. If something has $-3.2 \times 10^{-19}\ \text{C}$, you should instantly recognize that as $-2e$.

Conservation and net charge

Charge is conserved. It cannot be created or destroyed, only transferred.

• Net charge = algebraic sum of all charges.
• Neutral object → equal amounts of positive and negative charge.
• When you rub two objects together, you’re moving electrons, not creating charge.

This idea shows up in conceptual questions and in multi-step problems where charge redistributes.

Point charge model

A point charge is a model where the object’s size is negligible compared to the distance scale of the problem.

You treat all the charge as if it’s located at one point. On AP problems, unless geometry is clearly important, assume point charges.

2. Coulomb’s Law

The electric force between two point charges is given by:

$$F = k\frac{|q_1 q_2|}{r^2} = \frac{1}{4\pi \varepsilon_0}\frac{|q_1 q_2|}{r^2}$$

• $k = 9.0 \times 10^9\ \text{N}\cdot\text{m}^2/\text{C}^2$
• $\varepsilon_0 = 8.85 \times 10^{-12}\ \text{F/m}$
• $r$ = separation distance

Key features:

• Proportional to $q_1 q_2$
• Inversely proportional to $r^2$ → inverse-square law

If distance doubles, force becomes $\frac{1}{4}$. That sensitivity to distance is huge on tests.

Direction of the force

The force:

• Acts along the line connecting the charges.
• Like charges → repel
• Opposite charges → attract

And remember, force is a vector even though charge is scalar.

Newton’s Third Law

The force on charge 1 due to charge 2 has the same magnitude as the force on 2 due to 1, but opposite direction.

Students sometimes think a bigger charge “feels more force.” It doesn’t. Same magnitude, always.

Everyday forces come from electric forces

Normal force, friction, tension, elasticity. At the microscopic level, these are electric interactions between atoms. We model them as contact forces because tracking every charge would be impossible.

3. Multiple Charges and Superposition

When more than two charges are present, forces add vectorially.

Principle of superposition:
The net force on a charge equals the vector sum of the forces from each other charge.

How to solve these

1. Pick the charge you’re analyzing.
2. Draw each force vector carefully. Get directions right first.
3. Compute magnitudes using Coulomb’s law.
4. Break into components if needed.
5. Add vectors.

AP problems are limited to four or fewer charges unless there’s symmetry. If you see symmetry, use it. Forces often cancel cleanly.

4. Electric vs Gravitational Force

Both forces follow inverse-square laws.

Between two protons, electric repulsion is about $10^{36}$ times stronger than gravity.

So why does gravity dominate planets and stars?

• Large objects are usually electrically neutral.
• Positive and negative charges cancel.
• Gravity only attracts and cannot cancel.

Atomic scale → electric dominates.
Astronomical scale → gravity dominates.

5. Electric Permittivity and Polarization

Permittivity of free space

$\varepsilon_0$ appears in Coulomb’s law. It sets the strength of electric interactions in vacuum.

Smaller permittivity → stronger electric force.

Permittivity of materials

In matter, permittivity is:

$$\varepsilon = \varepsilon_r \varepsilon_0$$

Different materials respond differently to electric fields.

Electric polarization

When an external electric field is applied:

• Electron clouds shift slightly relative to nuclei.
• Tiny induced dipoles form.
• These dipoles create their own opposing field.

The diagram shows this at the microscopic level. On the left, with no external field $(E = 0)$, positive and negative charges are centered in each atom. On the right, when $E \ne 0$, the charges shift slightly, forming aligned induced dipoles.

Microscopic view of dielectric polarization

The stronger the polarization response, the higher the permittivity.

Conductors vs insulators

• Conductors: charges move freely. Internal electric field becomes zero in electrostatic equilibrium.
• Insulators (dielectrics): charges cannot move freely. They polarize instead.

This difference becomes critical later when you analyze fields and capacitors.