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2. Problem Set
Problem 1
A slab of volume charge of thickness d and permittivity H has free volume charge density
Pf Po sinax
and is confined between two perfectly conducting ground planes at infinite extent in the
x and z directions.
a) Find a particular solution to Poisson’s equation for the electric scalar potential.
b) If your solution to (a) does not satisfy the zero potential boundary conditions at y 0
and y d, add a homogeneous Laplacian solution, which does.
c) What is the electric field distribution for 0<y<d and what is the free surface charge
distribution on the y 0 and y d planes?
3. d) What is the equation of the electric field lines, defined as that goes through
the point ( o xy)?
e) Using your favorite graphics program, plot the electric field lines over the interval
Problem 2
A slab of volume current of thickness d and magnetic permeability has free volume current
density
and is confined between two perfectly conducting planes at y 0 and y d. The regions
for in the regions is filled with material of infinite magnetic permeability.
a) What is the magnetic field H in the regions in the regions ?
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4. b) What is the boundary condition on H at y d and y 0 inside the slab of volume
current ?
c) What is the magnetic field distribution for 0 < y < d and what is the free surface current
distribution on the y 0 and y d perfectly conducting planes?
d) What is the equation of the magnetic field lines?
e) Using your favourite graphics program, plot the magnetic field lines over the interval
f) How are the field lines of part 2e different than the field lines of problem 1e?
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33. f) In Problem 1e, electric field lines terminate perpendicularly to the electrodes on surface
charge. In Problem 2e, the magnetic field lines are parallel to the conducting walls
resulting in surface currents.
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34. Mathematica File for Computations Necessary to Generate Magnetic Field Vector Arrow
and Magnetic Field Line Plots
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