2.2
EEE 241Spring 2016
HW 1 Due January 19
Given A = ax-2ay+3az and B = ax+ay-2az, find the expression for a unit vector C
that is perpendicular to both A and B.
We can find the vector that is perpendicular to both these vectors by
EEE 241Spring 2016
HW 4Due February 9
3-10 Assuming that the electric field intensity is E = 100xax (V/m), find the total
electric charge contained inside (a) a cubical volume 100 mm on a side
centered symmetrically at t
EEE 241
Solution to Assignment #9
P.6-28
Consider the magnetic circuit in Figure 6-45. A current of 3(A) flows through 200 turns of wire
on the center leg. Asssuming the core to have a constant cross-sectional area of 103 (m2 ) and a
relative permeability
1.
EEE 241Spring 2016
HW 6 Due February 23
Work problem 3-34 from the textbook.
The coordinate system is cylindrical coordinates, and we can take the surface
charge on the inner coaxial cylinder as
Q
.
s =
2 ri L
Then, betwee
EEE 241Spring 2016
Final Exam Solutions
1.
A conducting sphere is located at the origin of the coordinate system. This sphere
has a uniform charge density such that the total charge is Q. The radius of the
sphere is a. Concentric with the sphere is a sphe
P.4-1
The upper and lower conducting plates of a large parallel-plate capacitor are separated by a distance d and maintained at potentials V0 and 0, respectively. A dielectric slab of dielectric constant 6.0 and uniform thickness 0.8d is placed over
EEE241 Fundamentals of Electromagnetics Spring 2007
Solutions to Homework 3
P3.5: Two point charges, Q1 and Q2 are located at (1,2,0) and (2,0,0) respectively. Find the relation between Q1 and Q2 such that the total force on a test charge at the p
EEE 241 Solution to Assignment #1
P.2-1
Given three vectors as follows, A = ax + ay 2 az 3, C = ax 5 az 2, nd (a) aA (c) A B (e) the component of A in the direction of C (g) A (B C) and (A B) C Solution: (a) aA =
A A
B = y 4 + az , a
EEE 241 Solution to Assignment #8
P.6-28
Consider the magnetic circuit in Figure 6-45. A current of 3(A) ows through 200 turns of wire on the center leg. Asssuming the core to have a constant cross-sectional area of 103 (m2 ) and a relative permeabi
The total outward flux of the E-field over any closed surface in free space is equal to
the total charge enclosed in the surface divided by 0 :
d =
0
This is a postulate of electrostatics: this is not a theorem
Provides a way to compute E alternative t
() = lim
Electric Field Intensity:
0
()
(V/m)
= q
(N)
Point, or Differential form
(valid in each point of space)
0
First postulate:
=
Second postulate:
=0
=
0
=
1
0
Static electric fields are not solenoidal
Static electric fields are irrotational,
=
40 2
E is a linear function of
2
: E(
1 1
1 2
+
2 2
2 2
For a system of n point charges:
1
=
40
1
2 ) + E(
2 2
2 2
)
z
( )
=1
3
+
2
2
3
3
+
2
2
(V/m)
For this system of 2 point charges
=
40
1 1
) = E(
+
2
+
2
+
2
2
3
3
+
2
2
=
40
2
3
=
2
far
= 0
Null Identity I:
If E is such that = 0, a V can be defined, such that
Physical significance:
work to be made against E to move q from P1 to P2 :
=
2 2 =
=
2
1
=0
Second postulate:
2
E is irrotational, or conservative
Physical significance:
man
An atom has a set of energy levels
Some (but not all) are occupied by electrons
energy
energy gap
increasing density
Gas
Solid
Graphics inspired by www.geo.umass.edu/probe/electronic%20structure.ppt
no interaction
outer levels interact
levels overlap
and
Dielectrics contain bound charges affecting the external electric field
External electric fields cause small displacements in positive and
negative bound charges within the dielectric material
The displacements create or modify existing dipoles that ar
z
Postulates of Electrostatics:
Coulomb Force:
=
B
F (q<0)
=0
=
q
(N)
(N)
Magnetic Force:
=
Lorentzs Force:
= q( + )(N)
x
F (q>0)
y
integral form
differential form
= 0
integrate over volume V
= 0
= 0
divergence theorem
= 0
= 0
integrate over
System: polarized dielectric (p ) plus free charges ( )
=
( + p )
=
0
0
p =
(0 + ) =
D=(0 + )
D =
(/2 )
= Electric Flux Density, or Electric Displacement, D
1) Info about bound charges has been moved inside D
2) Same form of first postulate, with
= +
=
= ( )
=
= = 2
1
1 2
=
=
=
2
2
1
1
=
=
=
2
2
2
=
1 2 1 2
+ 2
2
2
rate of decrease of electric and magnetic energy stored in V
minus ohmic power dissipated in V
divergence theorem
=
=
1 2 1 2
+
2
2
2
equals power l
(m/s)
for plane waves in a lossless medium = is a linear function of
phase velocity
=1
=
is independent of frequency
However, in many cases, is not a linear function of
If a signal is made of several plane waves, each wave will travel with its own p
2 + 2 = 0
Homogeneous wave equation, in frequency domain
=
Easy solution: all info is in = +
Issue: how to account for material response
= =
(m1 )
= + = 1 +
= + =
1
1
1
2
solution:
= =
2
Note: in a lossless medium
2 2 = 0
=
Traditional solut
=
one direction
linear polarization
= + ()= 0 0
two directions, same amplitude and phase
linear polarization
http:/youtu.be/oDwqUgDFe94
10 and 20 are denoting the amplitudes of the two
= 1 + 2 () = 10 20
, = Re
linearly polarized waves
1 + 2 () =
Source-free equation in free space:
1 2
2 2 = 0
A plane wave is a solution of Maxwells equations with
assuming the same direction, same magnitude, and
same phase in infinite planes perpendicular to the
direction of propagation. Similarly for .
Freque
A uniform plane wave characterized by = propagating in the+ direction has associated with
it a magnetic field = . Thus and are perpendicular to each other, and both are transverse
to the direction of propagation. It is a particular case of a transverse el