The Electric Field
The Electric Field (Cont.)
E
qtest
r
r
Q
rr
E (r ) =
Q
The electric field E (at a given point in space) is the force per unit
charge that would be experienced by the test charge at that point.
r
r
F( r )
E( r ) =
Electric Field
due to
Department of Electrical and Computer Engineering
ELEC 251 - Fundamentals of Applied Electromagnetics
Project # 2: Application of Friis Transmission Formula
Project Report Due Date: Thursday April 2, 2015 (during class)
1 Introduction
One of the fundament
Department of Electrical and Computer Engineering
ELEC 251 - Fundamentals of Applied Electromagnetics
Project # 1:
Application of Vector Calculus in Cylindrical and Spherical Coordinates
Project Report Due Date: Tuesday January 27, 2015 (during class)
1 I
Concordia University Department of Electrical and Computer Engineering
ELEC 251 Fundamentals of Applied Electromagnetics
Summer 2014
Instructor: Dr. D. Davis
Course Website: Accessed using MYCONCORDIA portal
Course Email: mcem352@yahoo.ca (Use this email)
Circuits vs Electromagnetics
Circuits
You have studied a number of devices
(resistors, capacitors, op amps, etc.)
and in order to make "connections"
between them, you have had to be certain
that they were solidly connected by
wire/solder/metal.
1
Set#1
E
Gausss Law: Electric flux ()
Properties:
r r
= D.dS
Surface
S is surface
of the box
Electric flux , is directly proportional
to the number of field lines passing through an area
Electric flux begins on positive charges and terminates on
negative charges
Magnetostatics (Chapter 5)
Magnetostatics is the branch of electromagnetics dealing with
the effects of electric charges in steady motion
(i.e, steady current or DC where d/dt = 0).
In magnetostatics, the magnetic field is produced by steady
currents.
Poissons and Laplaces Equations
Two approaches for finding E and V due to a given charge
distribution:
1st approach: given charge distribution, find E and V using
v ,
r
r
k v R dv
E ( R )=
R3
V=?
r
P r
& V ( at P) = E . d l
refernce
This method is val
Maxwells Equations for Time-Varying Fields (Chapt 6)
Faradays Law: Electromagnetic Induction
In the early 1830s Michael Faraday made the observation
that a changing current IP in one electric circuit can
cause current to appear (induce a current IS ) in
Magnetic Field of Toroid
Applying Amperes law over contour C:
Amperes law states that the line integral of
H around a closed contour C is equal to the
current traversing the surface bounded by
the contour.
-ve sign follows RHR
The magnetic field outside t
Intro
Welcome to Elec 251
Abdel R. Sebak
Intro
Room: EV 15.179
e-mail: abdo@ece.concordia.ca
Office Hours: Tu and Thu 10:00 am-12:00 noon,
or by appointment
1
Marking Scheme
One Scheme
Assignments
0
Quizzes
5
In-class Group Quizzes
5
Project
5
Midterm Tes
r
Magnetic Vector Potential A (5.4)
We can use the magnetic vector potential to calculate the magnetic field
(a 3rd approach complementing Amperes and Biot-Savarat Laws.
r
Electrostatics ( E
Definition
r
= 0)
Magnetostatics ( B
= 0)
r
A = Ax i + Ay j + Az
Section 4.4 - Gausss Law
r
r
Recall: Electric Flux Density
D = E [C/m 2 ]
r
r
Definition: Electric flux (
) =
D dS [C]
Surface
an
Properties:
D
Electric flux , is directly proportional
to the number of field lines passing through an area
Electric flux
Poissons and Laplaces Equations
Section 4.5.5
Two approaches for finding E and V due to a
given charge distribution:
1st approach: given charge distribution, find E and V using
v ,
r
r
k v R dv
E ( R )=
R3
V=?
r
P r
& V ( at P) = E . d l
refernce
This
Maxwells Equations for Time-Varying Fields
Faradays Law: Electromagnetic Induction
(Chapter 6)
In the early 1830s Michael Faraday made the observation
that a changing current IP in one electric circuit can
cause a current to appear (induce a current IS )
Poissons and Laplaces Equations
Section 4.5.5
Two approaches for finding E and V due to a
given charge distribution:
1st approach: given charge distribution, find E and V using
v ,
r
r
k v R dv
E ( R )=
R3
V=?
r
P r
& V ( at P) = E . d l
refernce
This
Section 4.4 - Gausss Law
r
r
Recall: Electric Flux Density
D = E [C/m 2 ]
r
r
Definition: Electric flux () =
D dS [C]
Surface
an
Properties:
D
Electric flux , is directly proportional
to the number of field lines passing through an area
Electric flux beg
ELECTROSTATIC BOUNDARY-VALUE
PROBLEMS (Chapter 6)
POISSONS & LAPLACES EQUATION
Given a closed dielectric region where the potential V is
specified on the boundary. Find V everywhere.
For a homogneous & linear medium:
. D = V , E = - V & D = E
. ( E) = .
Amperes Law of Force (Ch. 8)
Magnetostatics (Chapter 7 & 8)
Amperes Law Of Force and Biot-Savart Law
Amperes law of force is the law of action between
current carrying circuits.
Amperes Force law gives the magnetic force
between two current carrying cir
Example: Magnetic Field in a Solenoid
H
I
L
rr
H d l = HL
H
I
I enc = LnI ( n turns per unit length)
HL = LnI
I
H = nI
N
H I ( for finite solenoid)
L
H
Fields tend to cancel in region right between wires.
Field Lines continue down center of cylinder
Fiel
MAGNETIC FORCES AND TORQUES (Chapter 8)
MAGNETIC FORCES
Amperes Law of Force
Experimental facts:
Two wires carrying current in the same direction
attract.
Two wires carrying current in the opposite
directions repel.
A short current carrying wire orient
Magnetic Materials
Magnetization Vector
In the absence of an applied magnetic field, the magnetic
dipoles in most materials are randomly oriented, giving a
net macroscopic magnetization of zero.
When an external magnetic field is applied, the magnetic
d
Boundary Conditions For Magnetostatic Fields (Cont.)
Boundary Conditions For Magnetostatic Fields
Within a homogeneous medium, there are no abrupt changes in
H or B. However, at the interface between two different media
(having two different values of ),
Faradays Law:
Faradays Law: Electromagnetic Induction
The electromotive force, Vemf, induced around a closed loop L is equal
to the time rate of decrease of the magnetic flux linking the loop.
In the early 1830s Michael Faraday made the observation
Vemf =
Conductivity Range
ELECTRIC FIELD IN MATERIAL SPACE
(Chapter 5)
Silicon & Gemanium
Materials contain charged particles that respond to applied
electric and magnetic fields.
Materials are classified according to the nature of their response
to the applie
Hence, we have
Continuity Equation: Conservation of Charge
Electric charges can neither be created nor destroyed.
v
Since current is the flow of charge and charge is conserved:
there must be a relationship between the current flow out of a region
and t
Electric flux:
Electric Flux (Cont.)
Electric flux , is directly proportional to the number of
field lines passing through an area
Electric flux begins on positive charges and terminates
on negative charges
Flux is in the same direction as E.
Units of sa
Potential Energy
Energy to move a point charge through a Field
Work done by a force acting on an object moving along a path:
r
r
F = QE
Force on a charge in an electric field
dl
a
b
Differential work done by F moving Q:
(work is done against the field)
Magnetostatics (Chapter 5)
Magnetostatics is the branch of electromagnetics dealing with
the effects of electric charges in steady motion
(i.e, steady current or DC where d/dt = 0).
In magnetostatics, the magnetic field is produced by steady
currents.
Elec 251
Foundation of Electrostatics: Electric Charge
Matter is composed of
compact particles that carry
electric charge:
Electron & Proton
The charge on electron and proton are observed to
be equal and opposite.
The electron is said to have negative