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.
Express your answer in terms of the variables I, R, and appropriate constant (π).
B) Use Ampere's law to calculate the magnetic field B(r) for r≤R. Express your answers in terms of I.
Express your answer in terms of the variables I, R, r, and appropriate constants (μ0 and π).
C) Use Ampere's law to calculate the magnetic field B(r) for r≥R. Express your answers in terms of I.
Express your answer in terms of the variables I, R, r, and appropriate constants (μ0 and π).
I was able to figure out A) but I don't know how to use that answer for B) and C)
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