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A problem set from a university-level physics course, specifically phy 712. It asks students to find the vector potential and magnetic field of a current cylinder using the given formula for the current density. The problem involves calculating the vector potential and magnetic field for all ranges of radial distance (ρ) from the cylinder.
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February 28, 2007
PHY 712 – Problem Set # 15
Continue reading Chapter 5 of Jackson.
A current source has the form of a very long right circular cylinder of radius a oriented along the z axis as shown. The current density is uniform in the angular direction (φ), but varies along the radial direction (ρ) according to:
J(ρ) =
J 0 ˆz
( 1 − ρa
) 2 forρ ≤ a 0 forρ ≥ a
Find the vector potential A(ρ) and the magnetic field B(ρ) for all ranges of ρ.
