We can find Gravitational Potential Energy

rg ir

mmGF

2

21

i

ri

rF

Constr

mmGdr

r

mmGrU 21

221)(

0)( ConstU

r

rUF

r

rUFr

),(;

),(

r

mmGrU 21)(

Consider now a different type of a force…..

From long view of the history of mankind – seen from, say, ten thousand years from now – there can be little doubt that the most significant event of the 19th century will be judged as Maxwell’s discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the samedecade.

Richard P. Feynman

Nobel Prize in Physics, 1965

1918-1988

Consider a force like gravitation which varies as

but 1) billion-billion-billion-billion times stronger;

2) there are two kinds of “matter”: positive and negative; Like kinds repel and unlike kinds attract (unlike gravity where there is only attraction)

21

r

+ ++

_ _

_

Electrical force

All matter is a mixture of positive protons and negative electrons which are attracting and repelling with this great force.

How perfect is the balance?

-when you stand near someone else you don’t feel any force at all;

-if you were standing at arm’s length from someone and each of you had one percent more electrons than protons, the repelling force would be enough to lift a “weight” equal to that of the entire earth!

The force that holds atom together, and the chemical forces that holds molecules together, are electrical forces!

Atoms are made with positive protons in the nucleus and with electrons outside

This picture is obsolete!

If this electrical force is so terrific, why don’t the protons and electrons just get on top of each other?

Laws of quantum mechanics rule it out…

What holds the nucleus together?

A Helium Atom

-There are also nuclear forces – fall off much more rapidly than 21

r

An important consequence…..

Consider uranium with 92 (!) protons. The balance between the nuclear forces and electrical repulsion is so delicate that the nucleus is almost ready to fly apart. If we “tapped” it slightly……

Matter is effected by forces or interactions (the terms are interchangeable)

There are four fundamental forces in the Universe: gravitation (between particles with mass) electromagnetic (between particles with charge) strong nuclear force (between quarks) weak nuclear force (that changes quark types)

The atom contains a nucleus surrounded by a cloud of negatively charged electrons. The nucleus is composed of neutral neutrons and positively charged protons. The opposite charge of the electron and proton binds the atom together with electromagnetic forces.

Atom is mostly empty space!

Size of proton or neutron: ~10-15 m

Size of an electron cloud:~10-10 m (1 Angstrom)

Proton mass: 1.7x10-27 kgElectron mass: 9x10-31 kg

Magnify a hydrogen atom by 1210

the diameter of the electron cloud about 4.5 times longer than a football field

What holds a negatively charged electron together ?(since it has no nuclear force)

1909: Robert Millikan famous oil drop experiment

The smallest charge we ever observed is the “elementary charge”:

Coulombse 1910602.1

By convention, the electron has negative sign, the proton positive.

Electrostatics

• (the interactions of electric charges that are at rest in our frame of reference)

• There are two kinds of charge, positive and negative. Charges of the same sign repel each other; charges of the opposite sign attract.

• All ordinary matter is made of protons, neutrons, and electrons. The positive protons and electrically neutral neutrons in nucleus of an atom are bound together by the nuclear force.

Continue ….

• The negative electrons surround the nucleus at distances much greater than the nuclear size.

• Electric interactions are chiefly responsible for the structure of atoms, molecules, and solids.

Coulomb’s Law

Charge

Charge 1q

2q

2

21

04

1

x

qqFE

229229

0

/109/1094

1CmNcoulombmeterNewton

Conservation of electric charge

Charge is conserved: in any isolated system, the total charge cannot change. If it does change, then the system is not isolated: charge either went somewhere or came in from somewhere

0 is the permittivity of free space

qq

L

mg

T

x

y

xx maF 0sin EFT sinTFE

yy maF 0cos mgT

mgT coscos

mgT

tanmgFE

EF

qq

L

mg

T

x

y

If the length is 1 meter, q = 1Coulomb, what is mg?

NNL

qmg 992

2

0

106.155774.0

1109

tan)sin2(

1

4

1

Your weight? – Ns

mkg 7008.970

2

EF

030

qq

L

mg

T

x

y

tan)sin2(4

12

2

0

mgL

qFE

2

2

0

tan)sin2(

4

1

q

mgL

If we measure and know q and m, we can determine 04

1

EF

Exercise: If two electrons are placed meters apart, what is the magnitude of the Coulomb force between them? Compare this to the gravitational force between them.

810

Solution: The magnitude of electric force

NNx

qFE

1228

2199

2

2

0

103.2)10(

)106.1(109

4

1

22113119 /1067.6,1011.9,106.1 kgmNGkgmCq

The magnitude of gravitational force

NNx

mmGFG

5528

23111

221 104.5

)10(

)109(1067.6

43

210

2

104.5

3.2

4

mGm

q

F

F

G

E

(no matter what the separation is)

Principle of Superposition

The presence of other charges does not change the force exerted by point charges. One can obtain the total force by adding or superimposing the forces exerted by each particle separately.

Suppose we have a number N of charges scattered in some region. We want to calculate the force that all of these charges exert on some test charge .0q

1q2q

3q

4q

5q

6q

7q

8q

0q

.ˆ

4

1...

ˆˆ

4

1

12

0

02

2

2202

1

110

00

N

i i

iiq r

rqq

r

rqq

r

rqqF

Problem 2 page 9

Two equal, positive charges of magnitude are positioned along the x-axis as shown. What would be the force on a positive charge, , placed on the y-axis a distance H from the x-axis?

q

0q

H

q q

q0

x

y

a a

Have a great day!

Hw: All Chapter 1 problems and exercisesReading: Chapter 1, 2