•
Thursday Jan. 20, 2011
Dr. Andrew Brandt
Chapter 21
– Coulomb’s Law
– The Electric Field & Field Lines
– Electric Fields and Conductors
– Motion of a Charged Particle in an Electric Field
• Welcome HW is due Friday at 9pm
• Ch. 21Homework is due 9 pm, Thursday, Jan. 27.
It’s long so start right away!
• Labs start week of 31st
Thursday, Jan. 20, 2011 PHYS 1444-02 Dr. Andrew Brandt 1

• For grading purposes, some numeric answers to questions need to be exact.
For example, the answer to the question "How many days are in a week?" must be 7.
•The typical grading tolerance for most numeric answers in Mastering
assignment questions is between 2%-3%. For example, if the grading tolerance is
2% and the correct answer is 1043, both 1042 or 1045 are also graded as correct.
•When an answer is within tolerance, but doesn't match the correct answer: The officially correct answer displays in a purple box (provided that Show Whether Answer is Correct is set to Always). Students should use this answer if subsequent parts of an assignment item require calculations based on this answer.
•Students should use at least three digits or significant figures in answers, unless otherwise specified or unless the exact answer can be expressed using fewer than three significant figures. If higher precision is required, or lower precision is allowed, this is specified in the question or its instructions. When students must do multiple calculations to get an answer they should use more significant figures than required during each calculation and round off at the end
•You are allowed 4 attempts at a question (with each attempt you lose some points). Reread problem, could you have made a sign error or a unit error or a round-off error?
Thursday, Jan. 20, 2011 PHYS 1444-02 Dr. Andrew Brandt 2

F

Q
1 1
 r
2
Q
2 2
Formula F
 k
Q Q
1 2 r
• Is Coulomb force a scalar quantity or a vector quantity? Unit?
2
– 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 10 16 .
• Unit of charge is called Coulomb, C, in SI.
• The value of the proportionality constant, k , in SI units is k
  9 2
C
2
• Thus, if two 1C charges were placed 1m apart the force would be 9x10 9 N .
3

F
 k
Q Q r
2
2 Extremely
Similar
F

G
M M r
2
2
• 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
Thursday, Jan. 20, 2011 PHYS 1444-02 Dr. Andrew Brandt 4

• Elementary charge, the smallest charge, is that of an electron: e

1.602 10

19
C
– Since electron is a negatively charged particle, its charge is –e .
• Object cannot gain or lose fraction of an electron.
– Electric charge is quantized.
• It always occurs in integer multiples of e .
• The proportionality constant k is often written in terms of another constant,
1 4 e
e
0
0
, the permittivity of free space. They
1 4
 k
 
• Thus the electric force can be written:
F


12 2
C N m
1
4
e
• Note that this force is for “point” charges at rest.
0
Q Q
1 2 r
2
Thursday, Jan. 20, 2011 PHYS 1444-02 Dr. Andrew Brandt 5

• Electric force on electron due to proton. Determine the magnitude of the electric force on the electron in a hydrogen atom exerted by the single proton (Q
2
=+e) that is its nucleus. Assume the electron “orbits” the proton at its average distance of r = 0.53 x10 -10 m. (0.5 Angstrom)
Using Coulomb’s law
Each charge is
F

1
4
e
0
Q
1 e

Q Q
1 2 r
2
 k
Q Q
1 2 r
2

19
C and Q
2
  
1.602 10

19
C
So the magnitude of the force is
F
 k
Q Q
2 r
2
  9  2
C
2


8.2 10

8
N
Which direction?
Towards each other…
Thursday, Jan. 20, 2011 PHYS 1444-02 Dr. Andrew Brandt


19
C


10 m

2

19
C

Example on board
6

• Which charge exerts greater force? Two positive point charges, Q
1
=50 m C and Q
2
=1 m C, are separated by a distance L. Which is larger in magnitude, the force that Q
1 or the force that Q
2 exerts on Q
1
?
exerts on Q
2
Q Q
2 What is the force that Q
1 exerts on Q
2
?
F
12
 k
L
2
What is the force that Q
2 exerts on Q
1
?
F
21
 k
Q Q
1
L
2
Therefore the magnitudes of the two forces are identical!
Is there any difference?
What is the direction?
What is this law?
Thursday, Jan. 20, 2011
The direction.
Opposite to each other!
Newton’s third law, the law of action and reaction
PHYS 1444-02 Dr. Andrew Brandt 7

• Read and re-read problems carefully
• Draw a diagram using arrows to represent vectors
• Choose a convenient coordinate system
• Note the known and unknown quantities
• Write down the relevant relationships
• Do an approximate calculation
• Solve, substituting numbers only at the end
• Keep track of units
• Consider if answer is reasonable
Thursday, Jan. 20, 2011 PHYS 1444-02 Dr. Andrew Brandt 8


x
2
y
2

-1
y
x
Example on board
9 Thursday, Jan. 20, 2011 PHYS 1444-02 Dr. Andrew Brandt