EXTRA CREDIT LAB:
Report due Wednesday, November 3, 2004.
Objective
In this project you will use
Matlab's Partial Differential Equation Toolbox for modeling
magnetostatic phenomena.
This project has 3 parts. In Part 1, you will compare magnetic fields
calculated
from analytical and numerical models of a current carrying
wire. In
Part 2, you will model a permanent bar magnet. In Part 3, you
will
apply the model developed in Part 1, for calculating the magnetic
interference
fields generated from power lines. In Part 3, you will model a
permanent
bar magnet.
Part 1
A wire of radius 1 cm carries a current of 100 A, as shown in
Figure
1. Compute, analytically, the magnetic flux density
distribution in the region surrounding the wire. Plot magnitude of the
flux density as
a function of the distance from the wire.
Figure 1: Wire carrying current for Part 1.
Model the system using Matlab's PDE toolbox. You can download
the PDE
Toolbox tutorial here
(this has been provided to you as part of the pre-lab handout).Compare
the
magnetic flux density obtained from numerical simulation, with that
obtained
analytically. Comment on your results.
Part 2
Using the Matlab PDE toolbox simulate the magnetic field of a 4
cm
x 10 cm rectangular permanent bar magnet with a magnetic flux density
of
0.5 T (shown in Figure 2 below). Provide a detailed explanation
(including all the mathematics) of how you designed your model.
Figure 2: A permanent bar magnet showing the magnetic field lines
Part 3
Figure 3 below shows a pair of high voltage power lines adjacent to a
house.
Use the Matlab PDE toolbox to model this environment - choose
reasonable
dimensions and values for all geometric and field quantities. You can
assume
that the frequency of current flowing through the power lines is very
low
- and a static model provides a good approximation. Compute the
magnetic
fields in and around the power lines/house combination. Vary the
distance
between the pair of power lines and the house and the permeability of
the
house siding material and oberve the resulting field variations.
Provide
a detailed explanation (including all the mathematics) of how you
designed
your model. Use your simulation results to provide conclusions that you
have
drawn from this study.
Figure 3: High voltage power lines adjacent to a house.
Click here for the required lab
project report format.
