Electric Charge

Definition: Electric Charge

Electric charge is a fundamental property of matter which allows it to participate in electromagnetic interactions.

NOTATION

$$qQ$$

Unit of Measurement: Coulomb

The SI unit of measurement for electric charge is the Coulomb $[C]$ and it is fundamental.

Note: Algebraic Sign of Charge

An object may have positive $(q>0)$, negative $(q<0)$ or no $(q=0)$ electric charge.

Elementary Charge

Experiments show that electric charge is discrete. It appears that all objects in the universe are only allowed to possess charge which is an integer multiple of a very specific value, called the elementary charge.

Empirical Law: Elementary Charge

$$e=1.602176634\times 10^{-19}\mathrm{C}$$

Note: Charge of the Proton

The electric charge of the proton is $+e$.

Note: Charge of the Electron

The electric charge of the electron is $-e$.

This is explained by the fact that matter is composed of atoms and ions which in turn consist of protons, neutrons and electrons. So far, all evidence suggests that the electron lacks internal structure - it is elementary, not composed of anything else, and intrinsically has charge $-e$. The proton and neutron, on the other hand, are comprised of quarks and gluons. However, the charges of these constituents add up in such a way that the proton has a net charge of $+e$ and the neutron has no net electric charge.

Note: Electric Charges of Quarks and Gluons

Quarks possess fractional electric charge which is smaller in magnitude than the elementary charge $e$. However, quarks almost always appear in groups such that the net electric charge of the group is an integer multiple of $e$.

Gluons have no electric charge.

Conservation of Charge

Electric charge is a conserved quantity - the total amount of electric charge in a closed system remains constant in time.

Modelling Charged Objects

Discrete Charge Distributions

Oftentimes, we model an object which posses electric charge as a single point where all of the charge is concentrated.

Definition: Point Charge

A point charge is an idealisation of an electrically charged object which represents it as a single point with no size, where which all the object’s electric charge is concentrated.

This is a very rough approximation, but it turns out to be quite useful for most cases, especially when the distances between the objects involved are much larger than their size.

Continuous Charge Distributions

The electric charge of physical objects comes from the protons and electrons inside them. Since these are extremely small, we can view them as point charges and model the object they comprise as a collection of a huge number of point charges. However, keeping track of the positions of all individual protons and electrons is impossible. Instead, we can describe physical objects by how concentrated protons and electrons are around each point in the space they occupy.

Definition: Electric Charge Density

The electric charge density at a point $\mathbf{r}$ is a measure of how concentrated positive and electric charges are around $\mathbf{r}$.

We can consider different types of electric charge density depending on the type of region occupied by the object we are examining. Technically, all physical objects have occupy some volume. However, in many cases, some objects can be very accurately approximated as surfaces with surface area but no volume or as curved lines with length but neither surface area nor volume. For example, we can approximate a thin spherical shell as a surface with no thickness and we can approximate a wire as a line with length but neither surface area nor volume.

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