fall 2004 charge ece 2317: applied electricity and magnetism prof. valery kalatsky dept. of...
TRANSCRIPT
Fall 2004
Charge
ECE 2317: Applied Electricity and Magnetism
Prof. Valery KalatskyDept. of Electrical & Computer Engineering
University of Houston
Title
History
History
Charge was discovered by the Ancient Greeks (about 600BC) who found that rubbing fur on various substances, such as amber, would build up an electric charge imbalance.
The Greeks noted that the charged amber buttons could attract light objects such as hair.
The Greeks also noted that if they rubbed the amber for long enough, they could even get a spark to jump.
The word electricity derives from ηλεκτρον, the Greek word for amber.
More History
More History
Two glass rods rubbed with silk and placed near one another were observed to repel each other.
On the other hand, if a resin (plastic) rod rubbed with fur is placed near one of the glass rods, the force was attractive.
Benjamin Franklin (mid 1700’s) is credited with naming electrical charge; that appearing on the glass rod was designated positive and that on the resin (plastic) rod, negative.
Benjamin Franklin
Dr. Benjamin Franklin(January 17, 1706 — April 17, 1790)
American journalist, publisher, author, philanthropist, abolitionist, public servant, scientist, diplomat, and inventor.
One of the leaders of the American Revolution
He was well known also for his many quotations and his
experiments with electricity
Electric Charge
Electric Charge
Plastic rubbed with fur becomes negatively charged, glass rubbed with silk becomes positively charged.
Electric Charge
The phenomena of two objects sticking together can be explained by the notion that objects when rubbed can gain a net electric charge.
Electric Charge
There are two types of charge, labeled positive ( + ) and negative ( - ), with the following basic property:
• Like charges of the same sign repel each other.
• Unlike charges of the opposite sign attract each other.
Electric Charge
Electric Charge
Detailed experiments have established the following fundamental characteristics of electric charge:
e = 1.602 x 10 -19 Coulombs (C)
• Charge is never created nor destroyed - it is conserved.
This basic unit of charge is conventionally denoted by e :
• Charge always comes in an integral multiple of a basic unit - it is quantized.
The charge is conventionally denoted by q or Q
Electric Charge = Charge
Atom
proton: q = e = 1.602 x 10-19 [C]
electron: q = -e = -1.602 x 10-19 [C]
1 [C] = 1 / 1.602 x10-19 protons = 6.242 x 1018 protons
In an atom, the charge on an electron is - e and that on a proton is + e .
Hydrogen
Helium
Atom
1 Coulomb is a HUGE charge
t
1) Volume charge density v [C/m3]
v
V
[ ]v
Q
V
3C/m
uniform cloud of charge densityQ
Charge Density: Volume
VQ
t
0
, , limv V
Q dQx y z
V dV
v (x,y,z)
dV
non-uniform cloud of charge densitydQ
non-uniform (inhomogeneous) volume charge density
Charge Density: Volume
x, y, z – coordinates of the volume element
t
Charge Density: Volume
0
, , limv V
Qx y z
V
v (x,y,z)
dV
dQ
, ,v
Qx y z
V
, ,vQ x y z V
so , ,vdQ x y z dV
or
, ,v
V
Q x y z dV
t
Charge Density: Surface
2) Surface charge density s [C/m2]
s (x,y,z)
0lim [ ]s S
Q
S
2C/m
non-uniform sheet of charge density
Q
S
[ ]s
Q
S
2C/m
non-uniformuniform
t
Charge Density: Surface
, ,sdQ x y z dS
s (x,y,z)
dQ
dS
, ,s
S
Q x y z dS
[ ]s
dQ
dS 2C/m
t
Charge Density: Line
3) Line charge density l [C/m]
l (x,y,z)
0lim [ ]l l
Q
l
C/m
non-uniform line charge density
Q
l
non-uniformuniform
[ ]l
Q
l
C/m
++ + +
+ + +++++ + + +
t
Charge Density: Line
, ,ldQ x y z dl
+++
l (x,y,z)
Q
l+
+ + ++ + + + + + +
, ,l
C
Q x y z dl
t
, ,
10
10
v
V
V
V
Q x y z dV
dV
dV
x
y
z
av = 10 [C/m3]
Find: Q
3
10 V
4=10
3
Q
a
Example: Uniform Distribution
t
2
2
0 0 0
, ,
2
2 sin
v
V
V
a
Q x y z dV
r dV
r r dr d d
z
x
yav = 2r [C/m3]
Find: Q
22
0 0 0
4
sin 2
12 2
2
a
Q d d r r dr
a
Example: Non-Uniform Distribution
tt
z
x
yav = 3/r [C/m3]
Quiz: Non-Uniform Distribution
Find: Q
t