The cross-sectional area of one ring is given by: dA=2πrdr so that the current through one ring is given by: \[\begin{aligned} dI = j(r) dA = 2\pi a r^2 dr\end{a...The cross-sectional area of one ring is given by: dA=2πrdr so that the current through one ring is given by: dI=j(r)dA=2πar2dr The current through the whole wire is then found by summing the currents through each ring: I=∫dI=∫R02πar2dr=23πaR3
