Chapter 28, Problem 28.69P

CALC A long, straight wire with a circular cross section of radius R carries a current I. Assume that the current density is not constant across the cross section of the wire, but rather varies as J = αr, where α is a constant, (a) By the requirement that J integrated over the cross section of the wire gives the total current I, calculate the constant α in terms of I and R. (b) Use Ampere’s law to calculate the magnetic field B(r) for (i) r ≤ R and (ii) r ≥ R. Express your answers in terms of I.