Definition 21.1.1. 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.
