18-1

Physics IClass 18

Coulomb’s Law

Rev. 08-Mar-07 GB

18-2

Forces Known to Physics(Review)

There are four fundamental forces known to physics:

Gravitational Force (“yesterday’s news”) Electromagnetic Force (start today) Weak Nuclear Force Strong Nuclear Force

(All forces we observe are comprised of these fundamentalforces. Most forces observable in everyday experience areelectromagnetic on a microscopic level.)

18-3

A New Property of Matter -Charge

Charge comes in two types: positive and negative. NET charge can neither be created nor destroyed.

(Principle of Conservation of Charge) However, positive and negative charges can be separated or combined.

Charge is quantized – the smallest unit of charge (magnitude) innormal experience is the charge of the electron or proton, “e”.(All charges are integer multiples of this unit.)

By arbitrary historical convention, the charge of an electron is negativeand the charge of a proton is positive.

Neutral H

+e charge

electron

-e charge0 charge

proton

18-4

Conservation of Charge

neutron anti-neutrino

0 charge

proton

+e charge 0 charge

electron

-e charge

Charge is even conserved in nuclear reactions.

Here is what happens to a free neutron (outside anucleus) in about 12 minutes:

This is an example of the weak nuclear force (beta decay).

18-5

Coulomb - A Man, A Unit, A Law

Charles Coulomb, 1736-1806

Coulomb invented a delicate torsion balance withwhich he was able to measure the forces betweencharged and magnetic objects with sufficientaccuracy to verify a previous conjecture that themathematical formula for electromagnetic forceshould resemble the formula for gravity.

The unit of charge is named after Coulomb, abbreviated C.

1.0 C = 6.24150975 × 10+18 e1.0 e = 1.60217646 × 10–19 C

One Coulomb is a lot of protons!

18-6

Coulomb’s Law ofElectrostatic Force

)r(rqq

41

F 221

0

(Prof. B’s version – more later.)

The meaning of each term:

F: Electrostatic force on charge 1 from charge 2.

041:Electrostatic force constant = 8.98755 × 10+9 N m2/C2

1q: Value of charge 1, positive or negative.

2q: Value of charge 2, positive or negative.2r: Center distance from point charge 1 to point charge 2, squared.r: Unit vector from charge 1 to charge 2.

18-7

Direction of Electrostatic Force“Opposites Attract”

18-8

Properties of Electrostatic ForceSimilarities with Gravity

Every object with charge is attracted or repelled by every otherobject with charge. (Opposites attract, same repel.)

Electric force is a force at a distance (through occupied or emptyspace).

Electric force is a “central” force (center-to-center for pointcharges).

Electric force varies as the inverse square of the center distance. Electric force varies as the product of the charges.

18-9

Properties of Electrostatic ForceDifferences with Gravity

Electrostatic force is both attractive and repulsive,depending on the signs of charge.Gravity is always attractive.

There is only one sign of mass and no way to “cancelout” positive mass with negative mass.

A charged object can attract an object with no net chargeby causing polarization (a Physics 2 topic).

The electric force between a proton and an electron is farlarger than the gravitational force. (Next slide.)

18-10

Comparison of Gravity and Electrostatic Force

r = d i s t a n c e b e t w e e n p r o t o n a n d e l e c t r o n ( d o e s n ’ t m a t t e r )M = m a s s o f a p r o t o n = 1 . 6 7 2 5 2 × 1 0 – 2 7 k g .m = m a s s o f a n e l e c t r o n = 9 . 1 0 9 1 × 1 0 – 3 1 k g .G = g r a v i t a t i o n c o n s t a n t = 6 . 6 7 3 × 1 0 – 1 1 N m 2 / k g 2

e = c h a r g e o f p r o t o n ( + ) o r e l e c t r o n ( – ) = 1 . 6 0 2 1 7 6 4 6 × 1 0 – 1 9 C

041

= e l e c t r o s t a t i c c o n s t a n t = 8 . 9 8 7 5 5 × 1 0 + 9 N m 2 / C 2

C o n s i d e r i n g o n l y t h e r a t i o o f t h e m a g n i t u d e s :

mMG4

e

rmM

G

re

41

F

F

0

2

2

2

2

0

grav

elec 2 . 2 6 9 × 1 0 + 3 9

T h a t n u m b e r i s d i m e n s i o n l e s s –t h e s a m e e v e r y w h e r e i n t h e u n i v e r s e ( a s f a r a s w e k n o w ) .A d e e p m y s t e r y : W h y i s i t s o l a r g e ?

18-11

Superposition ofElectrostatic Forces

N

2ii2

i

i1

01on )r(

r

qq4

1F

(find and add X and Y components)

resultant

+1.0 C+5.0 C

resultant -3.0 C

+5.0 C

X

Y

1

18-12

Two Ways of Calculating theElectric Force Vector

Book Method: Find the magnitude of the force vector using the absolute

values of the charges. Use trigonometry and “opposite attract, like repel” to find

the direction. Convert to X, Y components.

Prof. B’s Method (Used in Computational Electromagnetics) A systematic method that will give you the X and Y

components without resorting to trigonometry or intuition. This will be described in the optional material at the end.

Use whichever method works best for you.

18-13

Class #18Take-Away Concepts

1 . C h a r g e s c o m e i n p o s i t i v e a n d n e g a t i v e .

2 . O p p o s i t e s c h a r g e s a t t r a c t , l i k e c h a r g e s r e p e l .

3 . C o u l o m b ’ s L a w o f E l e c t r o s t a t i c F o r c e

)r(r

qq4

1F 2

21

0

4 . S i m i l a r i t i e s a n d d i f f e r e n c e s w i t h g r a v i t y .

5 . T h e p r i n c i p l e o f s u p e r p o s i t i o n .

N

2ii2

i

i1

01on )r(

r

qq4

1F

18-14

Class #18Problems of the Day

___1. Three non-zero point charges are arrayed on a line asshown above. Qa has zero net electric force from Qb and Qc.Qc = +6.4 × 10-19 C and it is 2.0 cm from Qa. d = 1.0 cm.What is Qb?

A. Qb = –1.6 × 10-19 C.B. Qb = –3.2 × 10-19 C.C. Qb = –6.4 × 10-19 C.D. There is not enough information since Qa was not given.

Qb QcQa

2.0 cmd

18-15

Class #18Problems of the Day

2. Calculate the value in Coulombs of the total charge inAvogadro’s Number of protons. What would be the attractiveforce (magnitude) in Newtons on that much positive charge froman equal amount of negative charge one meter distant?

18-16

Activity #18Coulomb’s Law

(Another Pencil and Paper Activity)Objective of the Activity:

1. Think about Coulomb’s Law.2. Consider the implications of the Coulomb’s Law formula.3. Practice calculating electrostatic forces using superposition.

18-17

Class #18 Optional Material A Prof. B’s Method of Calculation

The next two slides will describe how to calculate the electricforce on a charge at a given point from another charge at adifferent point with a systematic procedure that is easier to usefor some people and also suitable for a computer. To use it,you need to understand how to manipulate vectors incomponent form.

18-18

How to Calculate aGeneral Unit Direction Vector

X8

Y

0

6

0

F r o m b l u e ( x 0 , y 0 ) t o r e d ( x , y ) :1 . F i n d t h e d i s p l a c e m e n t i n X , Y c o m p o n e n t s .

jˆ6i8jˆ)yy(i)xx(d 00

2 . F i n d t h e l e n g t h o f t h i s v e c t o r .

1068)yy()xx(|d|r 2220

20

3 . D i v i d e b y t h e l e n g t h t o g e t a u n i t v e c t o r .

jˆ6.0i8.010jˆ6i8rdr

A “unit vector” is a specialvector with dimensionlesslength of one unit.

18-19

How to Calculate the Electric Force Vector (Prof. B’s Method)

X8

Y

0

6

0

F o r c e o n b l u e c h a r g e ( x 0 , y 0 ) f r o m r e d c h a r g e ( x , y ) :1 . F i n d t h e v a l u e o f t h e s c a l a r p a r t o f t h e f o r m u l a :

221

0 rqq

41

F

( c o u l d b e + o r – )

2 . F i n d t h e u n i t v e c t o r f r o m b l u e t o r e d .T h i s w i l l b e i n X a n d Y c o m p o n e n t s .

3 . C h a n g e t h e s i g n o n b o t h c o m p o n e n t s .( T a k e s i n t o a c c o u n t l i k e c h a r g e s r e p e l . )

4 . M u l t i p l y F f r o m s t e p 1 t i m e s e a c h c o m p o n e n t f r o m s t e p 3 t o g e t f i n a l X a n d Y c o m p o n e n t so f f o r c e .

M a k e s u r e y o u a c c o u n t f o r a l l – s i g n s !

18-20

Class #18 Optional Material B“Three Quarks for Muster Mark”

We mentioned earlier that charge is quantized in units of +/– e.The charge of an electron is – e; the charge of a proton is +e.

Physicists now accept the Quark Theory, which holds that hadrons(elementary particles that interact with each other through the strong force)are composed of combinations of deeper fundamental particles:quarks.

Quarks have charges of +/– 1/3 e and +/– 2/3 e.

Let’s see why the Quark Theory was developed and how quarks form thebuilding blocks of protons and neutrons.

18-21

“Elementary” ParticlesAn Embarrassment of Riches

Joseph F. Alward, PhD Department of Physics University of the Pacific

Beginning with the discovery of the electron in 1898, physicists encountered an increasing array of so-called “elementary” particles. It became evident to physicists in the 1960’s that these particles must themselves be combinations of deeper fundamental particles.

18-22

The Origin of Quark Theory

Murray Gell-Mann tookthe name quark from "Three quarks for musterMark", in James Joyce'sbook Finnegan's Wake.(1963) (Nobel Prize 1969)

1929-In the early 1960’s, Gell-Mann and others proposed the Quark Theory to explain the “elementary” particles and their interactions in terms of 3 deeper fundamental particles called quarks.

Further developments have shown there are actually 6 different quarks and their corresponding anti-quarks. The quarks and their properties have been given whimsical names like “charm” that have no physical significance.

18-23

6 Quark Building Blocks

Quarks Anti-Quarks

Anti-Bottom