University of Pittsburgh
Department of Electrical Engineering
EE1259-Electromagnetics I
Fall 2012
Instructor: Prof. Kevin P. Chen
Coordinates:
Lecture room:
Email
Office
226 Benedum Hall
[email protected]
1136 Benedum Hall
Lectures:
Tuesday
Thursday
Office ho
EE1259 Calculus Problem Set III
Due at 4pm, Tuesday, September 29, 2015 in Class
Your Homework I include
Problem 1, 2, 4, 5, 6, 7,11
Please also work on other problems, you are not required to hand them in, but they are required in the first
mid-term.
1.
Course Notes for EE1259 Electromagnetics I
Vector Calculus
Vector Calculus:
Scalar triple product
(
)
(
)
(
r r r
r r r
r r r
A B C = C A B = B C A
Ax
r r r
A B C = Bx
Cx
(
)
Ay
a) Differentiated Lengthes:
r
r
r
dx a x + dy a y + dz a z
r
r
r
r
dl = d a
Course Notes for EE1259 Electromagnetics I
NOTES for Electrostatic Fields
This lecture covers Chapter 2-1, 2, 3
1. Coulumbs law
2. Electrical field induced by point charge
3. Electrical field due to continuous charge
distribution
Coulumbs Law:
a). Force b
University of Pittsburgh
ECE1259-Electromagnetics I
Fall 2015
Instructor: Prof. Kevin P. Chen
Lecture room:
Email
Office
226 Benedum Hall
[email protected]
1225 Benedum Hall
Lectures:
Tuesday
Thursday
Office hours:
4:00 pm to 5:15 pm
4:00 pm to 5:15 pm
Monday
Course Notes for EE1259 Electromagnetics I
NOTES for Vector Algebra
This is the 1st out of 5 lectures on math reviews
1.
2.
3.
4.
Unit vector, position vector, distance vectors
Vector addition and subtraction
Dot product
Cross products
Definition
A scala
EE1259 Calculus Problem Set II
1. Variables substitution: Given the same function in both cylindrical coordinate f(, , z) and in
spherical coordinate f(r, ,) prove that
f
f cos f
sin
r
r
f
f sin f
cos
z
r
r
EE1259: Calculus Problem Set II
1
2. Line
EE1259 Magnetostatic Homework #1
(Due on 5:15pm Nov 9, 2010)
1.
A hollow conducting cylinder has inner radius a and outer radius b and carries current I along the
positive z-direction. Find
Solution:
H everywhere.
Cylindrical coordinate symmetry:
Amperes
EE1259 Magnetostatic Homework #2
(Due on 5:15 pm Nov 16, 2010)
1. In a ferromagnetic material ( 4.50 ),
B 4 yaz
mWb / m2
Calculate m ,H,M,J b .
Solution:
m r 1 4.5 1 3.5
H
B
4 yaz
4 y 103 az
707.3 yaz A/m
4.50 4.5 4 107
M m H 3.5 707.3 yaz 2.476 yaz kA/m
EE1259 Assignment 5
(Due on 4:30 pm, Wednesday, March 5th, 2008)
1.
104 t
r
r
2
Given that J = 5e
a r A/m , at t=0.1 ms, find; (a) the amount of current passing surface r = 2m, (b) the charge
r
density v on that surface (assuming initial charge density is
EE1259 Assignment 6
1.
A large conduction cone (=45o) is placed on a grounded conducting plane with a tiny gap separating it from the
plane shown below. If the cone is connected to a 50-V source, find V, E, and surface charge density.
50V
=45o
gap
2.
A pa
EE1259 Assignment 4
1.
The electric flux density inside a dielectric sphere of radius a centered at the origin is given by
r
D = 0 ra r (C/m2)
Apply Gausss law to find volume charge density v.
2.
If the charge density increases linearly with distance from
10. Derive (a b ) b a a b
EE1259: Calculus Problem Set II
11
11. Derive
a) (u ) 0 where u is arbitrary scalar function;
b) ( a ) 0 where a is arbitrary vector function.
EE1259: Calculus Problem Set II
12
12. Derive (f g ) 0 if given ( F G ) G ( F ) F
EE1259 Calculus Problem Set II
Due at 4 pm on Tuesday, September 22, 2015 in Class
Your Homework II include
Problem 1, 2, 3, 4, 6, 9, 10, 12
Please also work on other problems, you are not required to hand them in, but they are required in the first
mid-t
EE1259 Calculus Problem Set I
Due at 4 pm on Tuesday, September 15, 2015 in Class
Your Homework I include
Problem 1, 4, 5, 6, 7, 8, 12, 13
Please also work on other problems, you are not required to hand them in, but they are required in the first
mid-ter
EE1259 Calculus Problem Set II
1. Variables substitution: Given the same function in both cylindrical coordinate f(, , z) and in
spherical coordinate f(r, ,) prove that
f
f cos f
sin
r
r
f
f sin f
cos
z
r
r
EE1259: Calculus Problem Set II
1
2. Line
EE1259 Calculus Problem Set III
1. Let R be the distance vector from a fixed point (x, y, z) to the point (x, y, z), let R to be its
length. Show that
a) R 2 2 R
a R R / R
b) 1 R R / R 3 a R / R 2
c) What is the general formula for R n
R
R
R
1
R
ay
:
f
D
:
A pp l y G n
:
1s s s l a w t o
=
P o r , (C
0 d c ha r gg de r u i i
yp
.
'
2
1e t B c
chmge dcns1
c o t e s w t 1d i n
g
i
i \ 1c e a s e s l i 11e a r 1y
v a r ia t o n o
w
ith di s t a n c e f r o m
r
3 r
4
,
t t t Ba t
p
w ln \ t
b
e\ &
or l
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EE1259 Calculus Problem Set I
1.
Four vectors drawn from a common point are given as follows:
A 2a x ma y a z
B max a y 2a z
C
ax ma y 2az
2
D m a x ma y a z
Find the value(s) of m for each of following cases:
(a) A is perpendicular to B
(b)
EE1259 Calculus Problem Set III
1. Let R be the distance vector from a fixed point (x, y, z) to the point (x, y, z), let R to be its
length. Show that
a) R 2 2 R
b) 1 R R / R 3 aR / R 2
aR R / R
c) What is the general formula for R n
R R R
1
R
R a x
EE1259 Electrostatics IV Solutions
Due at 4:00pm, Thursday, March 28th
1. Assume a BNC cable is manufactured with 2 different dielectrics. The first BNC cable
has dielectric one (1 = 2) filling the space between 0 , and a second dielectric
(2 = 3) fills t
EE1259 Electrostatics I Solutions
1. A line charge that lies along the x-axis starts at point x = -2 m and ends at the origin.
Given the linear charge density is = 3 ,find:
a. The total charge Q
3
0
= = 3 =
= 6 C
2
2
b. The electric field at th
EE1259 Electrodynamics and Magnetostatics Solutions
I
0
a
b
1. Show that the mutual inductance between the rectangular loop shown below and the
infinite line current is
b a 0
M 12 ln
2 0
2. The plane defined by x-y=1 separated medium 1 of permeability
EE1259 Electrostatics II Solutions
1.
The electric flux density inside a dielectric sphere of radius a centered at the origin is given by
r
D = 0 rar (C/m2)
Apply Gausss law to find volume charge density v.
2.
If the charge density increases linearly with
EE1259 Electrostatics Problem Set III
1. A sphere of radius a and dielectric constant r has a uniform charge density o, show that
a. At the center of the sphere:
2 1
6
b. Find the potential at the surface of the sphere.
2. Building a spherical charge o