Charge density

Also called Linear charge density, Surface charge density, Volume charge density

Charge density is the amount of electric charge per unit length, per unit area, or per unit volume of a charge distribution. Integrating it over the length, area or volume of the distribution returns the total charge.

AP Physics C: E&M states the whole requirement in one essential knowledge item. EK 8.6.A.5: if a function of charge density is given for a charge distribution, the total charge can be determined by integrating the charge density over the length (one dimension), area (two dimensions), or volume (three dimensions) of the charge distribution. The example it prints, which is also on the equation sheet, is

Q_{\text{total}} = \int \rho(\vec{r})\,dV

Spread over	Charge density	SI unit
A line	linear	C/m
A surface	surface	C/m $^2$
A volume	volume	C/m $^3$

Watch the symbols, because the sheet is thinner than your textbook. On the AP Physics C: E&M Table of Information, $\rho$ is defined as "resistivity or charge density" and it is the only charge-density symbol the sheet carries. Neither $\lambda$ for linear density nor $\sigma$ for surface density appears anywhere on it, so define them yourself if you use them on a free response. The CED's own phrase for the two-dimensional case, at EK 10.3.A.3.ii, is "surface charge density".

Where it does work. EK 10.1.A.3.iii says the charge density on a conductor's surface is greater at points and edges than on flat areas, and EK 10.3.A.3.ii makes the field between capacitor plates proportional to the surface charge density on either plate.

None of this is AP Physics 2. That CED never uses the term.

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