10.1 Electric Charge and Electric Force

Until 2024–25 this was taught in AP Physics 1. Now it's part of AP Physics 2, so the exam can test these basics directly.

Charge comes in two kinds, positive and negative. A proton carries +e, an electron carries −e, and a neutron has no charge. The elementary charge $e = 1.60 \times 10^{-19}$ C is treated as the smallest piece of charge there is, so every object's charge is a whole-number multiple of e. The unit of charge is the coulomb (C), which is a lot of charge; everyday static charges are usually microcoulombs (μC = 10⁻⁶ C) or nanocoulombs (nC = 10⁻⁹ C).

A point charge is a model where the charged object's size doesn't matter, because it's small compared with the distances involved. A charged sphere seen from far away works fine as a point charge.

The size of the electric force between two point charges is:

$$F_E = \frac{k\lvert q_1q_2 \rvert}{r^2}$$

Here $k = 9.0 \times 10^9$ N·m²/C², and r is the distance between the charges' centers. The force points along the line joining the two charges. Like charges repel and opposite charges attract.

The forces come in a Newton's third law pair: each charge pushes or pulls on the other with the same size force, in opposite directions, even if one charge is much bigger than the other.

• Double one charge: the force doubles.
• Double the distance: the force drops to 1/4.
• Halve the distance: the force becomes 4 times bigger.

When several charges act on one, find each force separately with Coulomb's law, then add them as vectors. Draw a free-body diagram first so the directions are clear, and break forces into x and y components if they aren't in a line. The exam keeps calculations to four or fewer charges, unless the arrangement is very symmetric.

Every object with mass and charge feels both gravity and electric force. For two protons, the electric force is about 10³⁶ times stronger than gravity. Electric forces can attract or repel, but gravity only attracts.

So why does gravity run the solar system? Large objects are almost perfectly neutral, so their positive and negative charges cancel and the electric forces nearly vanish. Mass never cancels, so gravity wins at large scales.

At everyday scales, contact forces like the normal force, friction and tension are really electric forces between huge numbers of atoms. It's just easier to treat them as their own forces.

In a conductor, like a metal, some electrons move freely. In an insulator, like rubber or glass, charges stay mostly in place. Even in an insulator, a nearby charge can shift electrons slightly within each atom or molecule, creating a separation of positive and negative charge called polarization.

Electric permittivity measures how easily a material polarizes in an electric field. Empty space has a fixed value, $\varepsilon_0 = 8.85 \times 10^{-12}$ C²/(N·m²), which shows up in many equations ($k = \frac{1}{4\pi\varepsilon_0}$). Other materials have different permittivities depending on how easily their electrons can rearrange.