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1
ECE 2317
Applied Electricity and Magnetism
Fall 2011
Homework #1
Date Assigned:
Jan. 20
Due Date:
Jan. 27
1.
A surface charge density
2
5( 1
)
s
xy
ρ
=
−
[C/m
2
] exists on the
xy
plane. Find the total
charge that lies within the rectangle defined by the vertices (0,0,0), (2,0,0), (2,1,0),
(0,1,0).
2.
A surface charge density
2
)
s
=
−
[C/m
2
] exists on the
xy
plane. Find the total
charge that lies within the triangle defined by the vertices (0,0,0), (1,0,0), (0,2,0).
3.
A slab of constant (uniform) charge density
0
vv
=
has a thickness
h
as shown
below, and is infinite in the
x
and
y
directions. Determine an effective surface charge
density
eff
s
(lying in the
xy
plane) that has the same amount of charge per unit area in
the
xy
plane as the slab of charge does.
4.
A cylindrical region of uniform charge density
0
=
having a radius
a
is shown
below. Determine an effective line charge density
eff
l
lying along the
z
axis that has
the same amount of charge per unit length (in the
z
direction) as the cylinder of
charge does.
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