Awire of circular cross-section carries current density that is not uniform but varies with distance from the center as j(r) = a r / r, for radius r in the range 0 < r < r. here, a is a constant with units amperes per square meter, and the radius of the wire is r = 8.1 mm. find an expression for the magnetic field outside of the wire, for r > r.

Students in an introductory physics lab are performing an experiment with a parallel-plate capacitor made of two circular aluminum plates, each 11 cm in diameter, separated by 1.0 cm. how much charge can be added to each of the plates before a spark jumps between the two plates? for such flat electrodes, assume that value of 3×106n/c of the field causes a spark.