Section 21.1 Charge Density
Subsubsection Key Ideas
Definition 21.1.2. Charge Density.
Charge density is the amount of charge in a given amount of space. It can be determined by dividing the small amount of charge \(dq\) in portion of an object by the size of that portion of the object. If the small portion of charge is a one-dimensional line (say, the \(x\)-direction), we would call it linear charge density
\begin{equation*}
\lambda = \frac{dq}{dx}
\end{equation*}
if the charge is on a two-dimensional surface, we would call it surface charge density
\begin{equation*}
\sigma = \frac{dq}{dA}
\end{equation*}
where \(dA\) represents a small area element and if the charge is in a three dimensional volume, we would call it volume charge density
\begin{equation*}
\rho = \frac{dq}{dV}
\end{equation*}
where \(dV\) represents a small volume element.
Just like for mass density, charge density describes how charge is distributed throughout a line, a surface, or a volume.
Subsubsection Activities
Activity 21.1.1. Sensemaking: Charge Density.
Determine the units for each charge density (one-, two-, or three-dimensional). Why are they different?
Explanation 21.1.2. Varying Charge Density.
Suppose you have a wire of length \(L\) with a charge density that changes from one side to the other. Describe in words why the total charge on your wire is NOT given by \(q = \lambda L\text{.}\)
