A certain wire has a circular cross section of radius \(R\) and carries a current \(I\). Suppose that the charge carriers all move along the cylindrical surface of the wire, not through its cross-sectional area.

(a) Derive an expression for the magnetic field magnitude \(B(r)\) as a function of distance \(r\) from the center of the wire; check that your expression makes sense for \(rR\).

(b) Make a graph showing the magnitude of the magnetic field in and around the wire as a function of the radial distance \(r\) from the center. Mark the wire radius \(R\) on your graph.