2. Electricity => Magnetism
In 1820, Prof. Oersted discovered that a
steady current produces a magnetic field
while teaching a physics class.
http://micro.magnet.fsu.edu/electromag/java/faraday/index.html
3. Would magnetism would produce
electricity?
Eleven years later, and
at the same time,
Mike Faraday in
London and
Joe Henry in New
York
discovered that a time-
varying magnetic field
produces an electric
current!
dt
d
N
Vemf
s
L
dS
B
t
dl
E
4. Electromagnetics was born!
This is the principle of
motors, hydro-electric
generators and
transformers operation.
s
L
dS
t
D
J
dl
H
*Mention some examples of em waves
This is what Oersted discovered
accidentally:
6. Some terms
E = electric field intensity [V/m]
D = electric field density
H = magnetic field intensity, [A/m]
B = magnetic field density, [Teslas]
m
H
m
F
H
B
E
D
o
o
/
10
4
36
10
/
10
85
.
8
7
9
12
7. Maxwell Equations
in General Form
Differential form Integral Form
Gauss’s Law for E
field.
Gauss’s Law for H
field. Nonexistence
of monopole
Faraday’s Law
Ampere’s Circuit
Law
v
D
0
B
t
B
E
t
D
J
H
v
v
s
dv
dS
D
0
s
dS
B
s
L
dS
B
t
dl
E
s
L
dS
t
D
J
dl
H
8. Moving loop in static B field
When a conducting loop is moving inside a magnet (static B
field), there’s a force on the charges.
http://www.walter-fendt.de/ph14e/electricmotor.htm
http://micro.magnet.fsu.edu/electromag/java/generator/dc.html
B
l
I
F
B
u
Q
F
Encarta®
9. Who was NikolaTesla?
Find out what inventions he made
His relation to Thomas Edison
Why is he not well know?
10. Vector Analysis Review:
What is a vector?
How to add them, multiply, etc,?
Coordinate systems
Cartesian, cylindrical, spherical
Vector Calculus review
11. Vector
A vector has magnitude and direction.
In Cartesian coordinates (x,y,z):
z
z
y
y
x
x A
A
A â
â
â
A
A
vector
unit
is
where
A
A
A
A
A
A
A
â
.
â
â
A
2
2
2
â
â
â
z
y
x
z
z
y
y
x
x
A
A
A
A
A
A
13. Example
Given vectors A=ax+3az and B=5ax+2ay-6az
(a) |A+B|
(b) 5A-B
(c) the component of A along y
(d) a unit vector parallel to 3A+B
Answers: (a) 7 (b) (0,-2,21) (c) 0 (d) ± (0.9117,.2279,0.3419)
14. Vector Multiplications
Dot product
Cross product
z
y
x
z
y
x
z
y
x
B
B
B
A
A
A
a
a
a ˆ
ˆ
ˆ
B
A
n
ABa
AB ˆ
sin
B
A
AB
AB
cos
B
A
z
z
y
y
x
x B
A
B
A
B
A
B
A
2
2
A
A
A A
Note that:
15. Also…
Multiplying 3 vectors:
Projection of vector A along B:
)
B
A
(
C
)
C
A
(
B
)
C
B
(
A
)
B
A
(
C
)
A
C
(
B
)
C
B
(
A
B
â
A
AB
Scalar:
Vector:
17. Cylindrical coordinates
f
f
f
sin
cos
tan 1
2
2
y
x
x
y
y
x
z
y
x
z
z
z
y
x
A
A
A
A
A
A
A
A
A
A
A
A
1
0
0
0
cos
sin
0
sin
cos
1
0
0
0
cos
sin
0
sin
cos
f
f
f
f
f
f
f
f
f
f
z
z
A
A
A â
â
â
A
f
f
19. Vector calculus review
Del (gradient)
Divergence
Curl
Laplacian
(del2 )
z
A
y
A
x
A z
y
x
A
z
y
x
z
y
x
A
A
A
z
y
x
a
a
a
ˆ
ˆ
ˆ
A
2
2
2
2
2
2
2
z
V
y
V
x
V
V
z
y
x a
z
a
y
a
x
ˆ
ˆ
ˆ
20. Theorems
Divergence
Stokes’
Laplacian
v
S
dv
S
d A
A
S
L
S
d
l
d
A
A
z
z
y
y
x
x a
A
a
A
a
A
z
V
y
V
x
V
V
ˆ
ˆ
ˆ
A 2
2
2
2
2
2
2
2
2
2
2
Scalar:
Vector:
Editor's Notes
Electrical Engineering, UPRM (please print on BOTH sides of paper)
Electrical Engineering, UPRM (please print on BOTH sides of paper)
Electrical Engineering, UPRM (please print on BOTH sides of paper)
Electrical Engineering, UPRM (please print on BOTH sides of paper)
Electrical Engineering, UPRM (please print on BOTH sides of paper)
Electrical Engineering, UPRM (please print on BOTH sides of paper)
Electrical Engineering, UPRM (please print on BOTH sides of paper)
Electrical Engineering, UPRM (please print on BOTH sides of paper)
Electrical Engineering, UPRM (please print on BOTH sides of paper)
Electrical Engineering, UPRM (please print on BOTH sides of paper)
