Fall 2004 Charge ECE 2317: Applied Electricity and Magnetism Prof. Valery Kalatsky Dept. of Electrical & Computer Engineering University of Houston TitleTitle.

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