Halliday, Resnick & Walker — Current and Resistance: Problem 1

1 The magnitude \(J(r)\) of the current density in a certain cylindrical wire is given as a function of radial distance from the center of the wire’s cross section as \(J(r) = Br\), where \(r\) is in meters, \(J\) is in amperes per square meter, and \(B = 2.00 \times 10^5 \text{ A/m}^3\). This function applies out to the wire’s radius of \(2.00 \text{ mm}\). How much current is contained within the width of a thin ring concentric with the wire if the ring has a radial width of \(10.0 \text{ }\mu\text{m}\) and is at a radial distance of \(0.750 \text{ mm}\)?