Weds., Jan. 15, 2014PHYS 1442-004, Dr. Andrew Brandt 1 PHYS 1442 – Section 004 Lecture #2...

Weds., Jan. 15, 2014 PHYS 1442-004, Dr. Andrew Brandt 1

PHYS 1442 – Section 004 Lecture #2

Wednesday January 15, 2014Dr. Andrew Brandt

1. Introduction 2. CH 16

--Coulomb’s Law--Vectors

Announcements

a)more than ¼ of the class has gotten started on mastering physics HW due Tues 21th. Next Hw due 28th will be posted soonb) if I send an email please read itc)Lab starts next week. my only association with the lab is I get your final lab grade at end of semester. d) read ahead

Weds., Jan. 15, 2014 2PHYS 1442-004, Dr. Andrew Brandt

Weds., Jan. 15, 2014 3

Why Do Physics?• To understand nature through experimental

observations and measurements (Research)• Establish limited number of fundamental laws, usually

with mathematical expressions• Explain and predict nature ⇒ Theory and Experiment work hand-in-hand⇒ Theory generally works under restricted conditions⇒ Discrepancies between experimental measurements

and theory are good for improvement of theory⇒ Modern society is based on technology derived from

detailed understanding of physics

Exp.{Theory {

PHYS 1442-004, Dr. Andrew Brandt

Weds., Jan. 15, 2014 4

Quiz (lets’ find out how many read ch 16)1) Did you read any of CH. 16?

2) Are my lecture notes on blackboard?

3) Have you used Clickers before?

4) Do you think we should get them for this class? Cost a problem?

5) If you double the charge on each of two equal magnitude charges and also double the distance between them, what happens to the electric force between them?


Weds., Jan. 15, 2014 5

Static Electricity and Electric Charge• Electricity is from Greek word elecktron=amber, a

petrified tree resin that attracts matter if rubbed• Static Electricity: an amber effect

– An object can become charged due to rubbing– Example: Rub feet on carpet and zap your little sister (Amber), if she’s not alert

• Two types of electric charge– Like charges repel while unlike charges attract– Ben referred to the charge on a glass rod as

positive, arbitrarily (and as it turns out incorrectly). Thus the charge that attracts a glass rod is negative. This convention is still used.


Weds., Jan. 15, 2014 6

Charge and Its Conservation• Franklin argued that when a certain amount of charge is

produced on one body in a process, an equal amount of opposite type of charge is produced on another body.– The positive and negative are treated algebraically so that during any

process the net change in the amount of produced charge is 0.• This is the law of conservation of electric charge.

– The net amount of electric charge produced in any process is ZERO!!• If one object or one region of space acquires a positive charge, then an equal

amount of negative charge will be found in neighboring areas or objects. • No violations have ever been observed.• This conservation law is as firmly established as that of energy or momentum.


Weds., Jan. 15, 2014 7

Electric Charge in the Atom• It has been understood through the past century that an atom

consists of – A positively charged heavy core What is the name?

• This core is the nucleus and consists of neutrons and protons.– Many negatively charged light particles surround the core What is

the name of these light particles?• These are called electrons• How many of these?

• So what is the net electrical charge of an atom?– Zero!!! Electrically neutral!!!

As many as the number of protons!!


Weds., Jan. 15, 2014 8

Insulators and Conductors• Picture two metal balls, one of which is charged• What will happen if they are connected by

– A metallic object?• Charge is transferred, until the charge is evenly distributed• These objects are called conductors of electricity.

– A wooden object?• No charge is transferred• These objects are called insulators.

• Metals are generally good conductors whereas most other materials are insulators.

• Atomically, conductors have loosely bound electrons while insulators have tightly bound electrons!


Weds., Jan. 15, 2014 9

Coulomb’s Law• Charges exert force on each other. What factors affect the

magnitude of this force?• Charles Coulomb figured this out in 1780’s.• Coulomb found that the electrical force is

– Proportional to the product of the two charges• If one of the charges is doubled, the force doubles.• If both of the charges are doubled, the force quadruples.

– Inversely proportional to the square of the distances between them.– Electric charge is a fundamental property of matter, just like mass.

• How would you put this into a formula?



• The value of the proportionality constant, k, in SI units is

• Thus, if two 1C charges were placed 1m apart the force would be 9x109N.

1 2Q QCoulomb’s Law – The Formula

• Is Coulomb force a scalar quantity or a vector quantity? Unit?– A vector quantity. Newtons

• Direction of electric (Coulomb) force is always along the line joining the two objects.– If two charges have the same sign: forces are directed away from each other.– If two charges are of opposite sign: forces are directed toward each other.

• Coulomb’s Law is accurate to 1 part in 1016.• Unit of charge is called Coulomb, C, in SI.

F 1Q 1 22

QQF k

r

2r 2Q Formul

a

9 2 28.988 10 N mk C


Coulomb’s Law – The MovieJust kidding?

https://sites.google.com/site/physicsflash/home/coulomb


Electric Force

• Does the electric force look similar to another force? What is it?– Gravitational Force

• What are the sources of the forces?– Electric Force: Charge, fundamental property of matter– Gravitational Force: Mass, fundamental property of matter

• What else is similar?– Inversely proportional to the square of the distance between the sources of the force

What is this kind law called?• Inverse Square Law

• What is different?– Gravitational force is always attractive.– Electric force depends on the sign of the two charges.– Magnitude

1 22

QQF k

r

and Gravitational Force1 2

2

M MF G

rExtremel

ySimilar


Example • Which charge exerts greater force? Two positive

point charges, Q1=50mC and Q2=1mC, are separated by a distance L. Which is larger in magnitude, the force that Q1 exerts on Q2 or the force that Q2 exerts on Q1?

1 212 2

QQF k

LWhat is the force that Q1 exerts on Q2?

Therefore the magnitudes of the two forces are identical!

Is there any difference? The direction.

What is the force that Q2 exerts on Q1? 2 121 2

Q QF k

L

What is this law?

What is the direction? Opposite to each other!

Newton’s third law, the law of action and reaction


Vector Problems • Calculate magnitude of vectors• Split vectors into x and y components

and add these separately, using diagram to help determine sign

• Calculate magnitude of resultant |F|=(Fx

2+Fy2)

• Use = tan-1(Fy/Fx) to get angle

Example on board


Vector Additions and Subtractions• Addition:

– Triangular Method: One can add vectors by connecting the tip of one vector to the tail of the other (tip-to-tail)

– Parallelogram method: Connect the tails of the two vectors and extend– Addition is commutative: Changing order of operation does not affect the results

A+B=B+A, A+B+C+D+E=E+C+A+B+D

A

BA

B=A

B

A+B

• Subtraction: – The same as adding a negative vector:A - B = A + (-B)

A-B

• Multiplication by a scalar increases the magnitude A, B=2A

A

B=2A

A+BA+B

A-B

OR

Weds., Jan. 15, 201416

Example for Vector AdditionA force of 20.0N applies to north while another force of 35.0N applies in the direction 60.0o west of north. Find the magnitude and direction of resultant force.

N

E

60o

θF20F1

F2

60cos0.350.2020.350.20 22

60cos0.350.20

60sin0.35tan 1

N W wrt to9.385.37

3.30tan 1

F2cos60o

F2sin60o


Weds., Jan. 15, 2014 17

Components and Unit VectorsCoordinate systems are useful in expressing vectors in their components

(Fx,Fy)F

θ

Fy

Fx

x

y

}Components

(+,+)

(-,+)

(-,-) (+,-) } Magnitude



Unit Vectors• Unit vectors inddicate the directions of the

components• Dimensionless • Magnitudes are exactly 1• Unit vectors are usually expressed in i, j, k or

So the vector F can be re-written as

Weds., Jan. 15, 2014 19

Announcements• Monday is a holiday so next class is Weds. 22nd• What Holiday?• Read Ch. 16 before next class • Enroll in Mastering Physics and do first “welcome”

assignment• Read Book, Do HW, Go to Lab, Learn Physics• Good grade will follow


Weds., Jan. 15, 2014PHYS 1442-004, Dr. Andrew Brandt 1 PHYS 1442 – Section 004 Lecture #2...

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