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PHY 712 Problem Set #15: Vector Potential and Magnetic Field of a Current Cylinder - Prof., Assignments of Electromagnetism and Electromagnetic Fields Theory

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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Pre 2010

Uploaded on 08/19/2009

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February 28, 2007
PHY 712 Problem Set # 15
Continue reading Chapter 5 of Jackson.
1. A current source has the form of a very long right circular
cylinder of radius aoriented along the zaxis as shown.
The current density is uniform in the angular direction
(φ), but varies along the radial direction (ρ) according
to:
J(ρ) =
J0ˆz ³1ρ
a´2forρa
0 forρa(1)
Find the vector potential A(ρ) and the magnetic field
B(ρ) for all ranges of ρ.

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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.