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ECE 2317
Applied Electricity and Magnetism
Exam 1
Oct. 20, 2011
1. This exam is closed book and closed notes. Calculators, but no other
electronic devices, are allowed.
2. Show all work. No credit
ECE 2317
Applied Electricity and Magnetism
Fall 2012
Homework #5
Date Assigned: Oct. 2, 2012
Due Date: Oct. 9, 2012
1) A planar slab of charge shown below has a charge density
v
=
cos x,
2
<x<
2
.
Find the electric field vector in all regions, using Gaus
Electromagnetics Workshop Final Review
Final Review Problems & Solutions
Problem 1:
A cylindrical capacitor with inner radius a and outer radius b is filled with an inhomogeneous
dielectric having = 0 k , where k is a constant. Calculate the capacitance p
Dielectrics
ECE 2317
Applied Electricity and Magnetism
Under microscope:
H+
Fall 2006
+
+
water
Prof. Filippo Capolino
ECE Dept.
H2O
= 0 r

O
+
Notes prepared by the EM group,
University of Houston.
(used by Dr. Jackson, spring 2006)
Dielectrics (cont.
Gradient
ECE 2317
Applied Electricity and Magnetism
( x, y, z ) = scalar function
Fall 2006
grad x
Prof. Filippo Capolino
ECE Dept.
+y
+z
x
y
z
grad = x + y + z
y
z
x
Notes 17
grad =
Notes prepared by the EM group,
University of Houston.
(used by Dr.
Curl of a Vector
ECE 2317
Applied Electricity and Magnetism
V ( x, y, z ) = vector function
Fall 2006
1
s 0 S
1
y curl V lim
s 0 S
1
z curl V lim
s 0 S
x curl V lim
curl V = vector function
Prof. Filippo Capolino
ECE Dept.
z
S
Cz
Cx
Cy
Cz
V dr
V dr
V dr
S
ECE 2317
Applied Electricity and Magnetism
Potential Integral Formula
This is a method for calculating the potential function directly,
without having to calculate the electric field first.
Fall 2006
Prof. Filippo Capolino
ECE Dept.
This is often the easi
Potential Calculation
ECE 2317
Applied Electricity and Magnetism
r=B
C
Fall 2006
B
VAB = E dr
R=A
Prof. Filippo Capolino
ECE Dept.
A
= ( A) ( B )
r
( R ) ( r ) = E dr
Hence:
R
Notes 14
r
( r ) = ( R ) E dr
Notes prepared by the EM group,
University of H
Divergence  Physical Concept
ECE 2317
Applied Electricity and Magnetism
Start by considering a sphere of uniform volume charge density
The electric field is calculated using Gauss's law:
Fall 2006
Prof. Filippo Capolino
ECE Dept.
r < a:
z
D n dS = Q
v =
ECE 2317
Applied Electricity and Magnetism
Fall 2006
Prof. Filippo Capolino
ECE Dept.
Notes 12
Notes prepared by the EM Group,
University of Houston
(used by Dr. Jackson, spring 2006)
Example
Example
x
s0B
x = d/2
y
s0 A
x =  d/2
(a)
(b)
(c)
x > d/2
d/2
Example
ECE 2317
Applied Electricity and Magnetism
z
Find the electric field everywhere
Fall 2006
D n dS = Q
encl
Prof. Filippo Capolino
ECE Dept.
S
r
h
y
Assume
S
x
Notes 11
D = D ( )
l = l0 [C/m]
Notes prepared by the EM group,
University of Houston.
(
ECE 2317
Applied Electricity and Magnetism
z
Gausss Law
S (closed surface)
The charge q is inside the surface
Fall 2006
Prof. Filippo Capolino
ECE Dept.
q
y
= N ( all flux lines go through S )
x
Notes 10
E
q
N flux lines
D n dS = q
Notes prepared by the
Flux Density
ECE 2317
Applied Electricity and Magnetism
E=
E
Fall 2006
Prof. Filippo Capolino
ECE Dept.
q
q
4 0 r 2
r
Define:
D 0 E
Notes 9
D=
Notes prepared by the EM group,
University of Houston.
(used by Dr. Jackson, spring 2006)
flux density vector
q
ECE 2317
Applied Electricity and Magnetism
Fall 2012
Homework #11
Date Assigned: Tuesday, Nov. 20, 2012
Due Date: Thursday, Nov. 29, 2012
1. The specific heat s of a material in [J / (kG deg C)] is the amount of energy in Joules required
to raise the temp
ECE 2317
Applied Electricity and Magnetism
Fall 2012
Homework #10
Date Assigned: Tuesday. Nov. 13
Due Date: Tuesday, Nov. 20
1) A parallelplate capacitor has one plate (at x = 0) at zero volts and the other plate (at x = h) at
V0 volts. Inside the capaci
ECE 2317
APPLIED ELECTRICITY AND MAGNETISM
Fall 2012
Homework #9
Date Assigned: Tuesday, Nov. 6
Due Date: Tuesday, Nov. 13
1) A parallelplate capacitor has a separation of 2 [mm] between the plates. Oil is used as the
insulating material between the plat
ECE 2317
Applied Electricity and Magnetism
Fall 2012
Homework #8
Date assigned: Oct. 20, 2012
Date due: Nov. 6, 2012
1) Under normal conditions, can the relative permittivity of a material ever be less than 1.0? If
not, give a convincing explanation of wh
ECE 2317
Applied Electricity and Magnetism
Spring 2012
Homework #7
Date assigned: Oct. 23, 2012
Date due: Oct. 30, 2012
1) Find the curl of the following vector functions:
V = x ( 5 x 2 yz ) y ( e y x ) + z ( 3xyz 2 )
V = ( cos ) ( 3 z sin ) + z ( z )
V=
ECE 2317
Applied Electricity and Magnetism
Fall 2012
Homework #6
Date Assigned: Oct. 9, 2012
Due Date: Oct. 16, 2012
1) A spherical shell of uniform surface charge density s0 has a radius a. Find the potential at the
center of the sphere, assuming that th
ECE 2317
Applied Electricity and Magnetism
Fall 2012
Homework #4
Date Assigned: Sept. 25, 2012
Due Date: Oct. 2, 2012
1) Make a flux plot for the case shown below, which has two infinite line charges (l0 on the left
and l0 on the right). The equipotentia
ECE 2317
Applied Electricity and Magnetism
Fall 2012
Homework #3
Date Assigned: September 18
Due Date: September 25
1. Point charge 1 having 2 [C] is at the point (1,2,3) [m] in space. Point charge 2 having 3 [C]
is at the point (1,4,2) [m] in space. Fi
ECE 2317
Applied Electricity and Magnetism
Fall 2012
Homework #2
Date Assigned: Sept. 11
Due Date: Sept. 18
1. Derive the identity= cos + ( sin ) .
x
2. Derive the identity x cos cos + y cos sin + z ( sin ) .
=
3. An electric field is described = y ( 2 y
ECE 2317
Applied Electricity and Magnetism
Spring 2012
Homework #1
Date Assigned: Aug. 30
Due Date: Sept. 6
1. A surface charge density s 5 x 2 ( y 1) [C/m2] exists on the xy plane. Find the total
=
charge that lies within the rectangle defined by the ver
Boundary Value Problem
ECE 2317
Applied Electricity and Magnetism
Goal:
Solve for the
potential function
inside of a region,
given the value of the
potential function on
the boundary.
Fall 2006
Prof. Filippo Capolino
ECE Dept.
Notes 21
2 ( x, y , z ) = 0
ECE 2317
Applied Electricity and Magnetism
Fall 2006
Boundary Conditions for Dielectrics
Tangential component
of electric field:
z
Ex1
1
2
Prof. Filippo Capolino
ECE Dept.
A
Ex2
Notes prepared by the EM group,
z = 0+ : VAB Ex1x
Boundary Conditions (cont.)
Example
ECE 2317
Applied Electricity and Magnetism
z
r = (0, 0, z)
R
Fall 2006
Prof. Filippo Capolino
ECE Dept.
Find
s = s0
a
E (0, 0, z)
[C/m2]
y
b
x
dS ' = ' d ' d '
R = ' ( ') + z z
y
d
Notes 8
R = '2 + z 2
dS
x
Notes prepared by the EM group,
R=
Unive
Coulombs Law
ECE 2317
Applied Electricity and Magnetism
z
Experimental law:
r
Fall 2006
r
Prof. Filippo Capolino
ECE Dept.
F2 =
q2
q1q2
r
4 0 r 2
[ N]
0 = 8.854187818 1012
y
[ F/m]
q1
x
Note: c = speed of light = 2.99792458108 [m/s] (exactly)
Notes 7
Not
Solution of Laplaces Equation by Finite Differences
By:
Carlos Moran
PS Number: 0429409
For:
ECE 2317: Applied Electricity and Magnetism (Fall 2007)
Instructor:
Ji Chen
Task 1
Task 1 required to find the potential on each node inside of the box. To this I
Mock Exam #1 Solutions
Problem 1:
An electric field is defined in rectangular coordinates as
E = xx + 3 yy [V/m]
(This is a valid electrostatic field.) Calculate the voltage drop VAB , where A is the point (0,0,0) and
B is the point (1,1,0) in rectangular