Obtain an expression to show that the change in the quantity of charge enclosed in an arbitrary volume is accompanied by a net flow of charge inwards or outward across the surface of the enclosed volume.

The relationship between electric and magnetic phenomena in the context of charge distribution is described by the continuity equation, which establishes a connection between the change in the quantity of charge enclosed within a volume and the flow of charge across the surface of that volume.

To begin, consider a region of space bounded by a closed surface \( S \), and let the volume enclosed by this surface be denoted as \( V \). The charge density within this volume is represented by \( \rho(\mathbf{r}) \), where \( \mathbf{r} \) denotes a point in space. The total charge enclosed within the volume \( V \) at any time \( t \) can be written as:

\[
Q_{\text{enc}}(t) = \int_V \rho(\mathbf{r}, t) \, dV
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