This preview shows page 1. Sign up to view the full content.
ECE 230B, HW1, Winter 2010
1.
3D Gauss’ law is obtained after a volume integration of 3D Poisson’s equation and
takes the form of
E
⋅
=
∫∫
dS
Q
si
S
ε
,
where the LHS is an integral of the normal electric field over a closed surface
S
, and
Q
is the net
charge enclosed within
S
.
Use it to derive the electric field at a distance
r
from a point charge
Q
(Coulomb’s law).
What is the electric potential in this case?
2.
(a) Use Gauss’ law to show that the electric field at a point above a uniformlycharged
sheet of charge density
Q
s
per unit area is
Q
s
/2
, where
is the permittivity of the medium.
(b) For two oppositelycharged parallel plates with surface charge densities
Q
s
and

Q
s
,
show that the electric field is uniform and equals
Q
s
/
in the region between the two plates, and
is zero in the regions outside the two plates.
3.
Assume silicon, room temperature, complete ionization. An abrupt pn junction with N
a
=
N
d
= 10
17
cm
3
is reversed biased at 2.0 V.
This is the end of the preview. Sign up
to
access the rest of the document.