AP Physics C: Electricity and Magnetism

## Charge Charge is a fundamental property of matter, and it comes in two kinds, called positive and negative. It is a scalar, so it is added as an ordinary number with its sign, but the sign carries information: it decides whether two objects attract or repel. The SI unit is the coulomb (C). Charge is quantised. The smallest free charge is the magnitude of the charge on an electron or a proton, the elementary charge $$ e = 1.60 \times 10^{-19}\ \mathrm{C} $$ An electron has charge $-e$, a proton has $+e$ and a neutron has no charge. Any charge on an object is a whole-number multiple of $e$. Because $e$ is so small, the charges met in laboratory work (microcoulombs and nanocoulombs) contain enormous numbers of electrons, and treating charge as continuous is an excellent approximation when a distribution is being integrated over. A **point charge** is a model in which the object's size is negligible compared with the distances in the problem. A charged sphere with its charge spread evenly behaves, outside its surface, as if all its charge were at its centre, so a sphere can be treated as a point charge when the other objects are outside it. ## Coulomb's law Two point charges $q_1$ and $q_2$ a distance $r$ apart exert forces on each other that are equal in size and opposite in direction, along the line joining them. The magnitude grows in direct proportion to each charge and falls with the square of the distance between them. $$ F = \frac{1}{4\pi\varepsilon_0}\,\frac{\lvert…