Final Exam: Problem #4

 

Statement of Problem 4

Solution to the Problem

Part A

I began by using the Bland Starter Program in directory:

 ~bland/public_html/courses/703/hw/np0502/blines.pro

The graph depicts a solid (a=0) cylindrical wire with permeability mu (=10) in a uniform magnetic field, b0, with the axis of the wire perpendicular to the field.

Letting the wire have a high permeability such as mu=600 (graph), where is the absolute value of the perturbed magnetic field outside the wire the greatest? After adding new code to the program, the magnitude of the perturbed magnetic field outside the wire was found to be greatest at rho=1.00056, and theta=0.0518629. (In cartesian coordinates: x=0.999211 and y=0.0518685) The magnitude of the field is: B=0.199288. This is 1.99288 times greater than B0.

Part B

What if the wire is a superconducting wire? A superconductor has no resistance and no magnetic field in its volume. The earlier program can be adjusted so that the cylindrical material is a superconduction wire by setting mu=0.

Running the program reveals the magnitude of the perturbed magnetic field outside the superconducting wire to be greatest at rho=1.89887, and theta=1.58644. (In cartesian coordinates: x=-0.0296982 and y=1.89864) The magnitude of the field is: B=0.127723. This is 1.27723 times greater than B0.