Students, pretending they are point charges, move around the room so as to make an imaginary magnetic field meter register a constant magnetic field, introducing the concept of steady current. Students act out linear \(\vec{I}\), surface \(\vec{K}\), and volume \(\vec{J}\) current densities. The instructor demonstrates what it means to measure these quantities by counting how many students pass through a gate.

Current \(I\) flows down a wire (length \(L\)) with square cross-section (side
\(a\)). If it is uniformly distributed over the entire area, what is the
magnitude of the volume current density \(\vec{J}\)?

If the current is uniformly distributed over the outer surface only, what is the
magnitude of the surface current density \(\vec{K}\)?

A current \(I\) flows down a cylindrical wire of radius \(R\).

If it is uniformly distributed over the surface, give a formula for
the surface current density \(\vec K\).

If it is distributed in such a way that the volume current density,
\(|\vec J|\), is inversely proportional to the distance from the axis,
give a formula for \(\vec J\).

A solid cylinder with radius \(R\) and height \(H\) has its
base on the \(x,y\)-plane and is
symmetric around the \(z\)-axis. There is a fixed volume charge density
on the cylinder \(\rho=\alpha z\). If the cylinder is spinning with period \(T\):

The current density in a cylindrical wire of radius \(R\) is given by
\(\vec{J}(\vec{r})=\alpha s^3\cos^2\phi\,\hat{z}\). Find the total current in the wire.

Students calculate electrostatic fields (\(V\), \(\vec{E}\)) and magnetostatic fields (\(\vec{A}\), \(\vec{B}\)) from charge and current sources with a common geometry. The sequence of activities is arranged so that the mathematical complexity of the formulas students encounter increases with each activity. Several auxiliary activities allow students to focus on the geometric/physical meaning of the distance formula, charge densities, and steady currents. A meta goal of the entire sequence is that students gain confidence in their ability to parse and manipulate complicated equations.