Welcome to Physics 112N

1
Welcome to Physics 112N

• Professor Charles E. Hyde-Wright
• Spring 2005
• Navigate from httpwww.physics.odu.edu, or
• httpwww.physics.odu.edu/hyde/Teaching/Spring05/Ph
  ys112_2005.htm

2
Topics to be covered

• Electricity and Magnetism (Chapters 19-24)
• Light and Optics (Chapters 25, 26, 28)
• Modern Physics (Chapter 30)

3
Phys 111 Chapters 1-18

• Description of motion Kinematics
• Position (in 1-, 2-, 3- dimensions)
• Velocity (rate of change of position)
• Acceleration (rate of change of velocity)
• Relationship between Force and Motion
• Net Force equals mass times acceleration
• Description of motion in terms of Energy
• Kinetic Energy
• Potential Energy (Gravity, Springs)
• Thermal Energy (non conservative forces)
• Examples of forces
• Contact forces (friction, normal force force
  perpendicular to surface)
• Spring Force F - kx
• Gravity

4
Gravity

• F G M m / r2
• Near surface of earth ( h ltlt R )
• F G M m /(Rh)2 ? m GM/R2 mg
• Circular, Elliptical, Parabolic, Hyperbolic
  orbits of moons, planets, asteroids, comets,
  possible visitors from outer space.
• Potential Energy
• U - G M m /r
• Note minus sign, Potential energy decreases as
  two masses approach Conservation of energy
  means Kinetic Energy increases as Potential
  energy decreaces.

5
Chapter 19 Electric Charges, Forces, and Fields

• Fundamental Forces in Physics
• Gravity (gravitons)
• Electromagnetism (photons)
• Weak Interaction (W and Z bosons)
• Strong Interaction (gluons)
• All of physics is based on these four forces
• All four forces have similar equations.

6
Energy in our World

• Nuclear Fusion in sun Emc2
• H H H H ? He n n Energy
• Thermal Energy at surface converted to visible
  light energy
• Light Energy ? Chemical Energy (photosynthesis)
• Plants ? Fossil Fuels
• Fuel for cars (motion)
• Fuel for power plants
• (electrical energy ? lighting for your Physics
  HW).
• Plants ? Food gt Krebs cycle ADP/ATP
• Energy for thought, motion of muscles ? HW

Fusion
Radiation
7
Electromagnetism in our World

• Gravity holds us to the earth.
• Electromagnetism dominates every other aspect of
  our physical world
• Atoms, Molecules, Solids, Liquids held together
  by electrostatics
• Chemistry
• Light
• Virtually all technology
• Electronics, Electric motors, Electric Lighting
• Even fire is fundamentally an electromagnetic
  phenomenon
• Profound insights into the physical nature of
  life.

8
Electrostatic Phenomena

• Rubbing things makes an electrostatic charge
• Spark, Hair standing on end
• Thunderclouds rub rising microscopic ice-crystals
  against falling hail ? Clouds charge up
• Electrostatic phenomena do not require any
  obvious macroscopic change (mass, material change)

9
Basic Model of ElectrostaticsFranklin, Coulomb,
18th Century

• When two dissimilar materials are in contact,
  microscopic particles can be transferred from one
  to the other
• Modern view electrons e-, or ions Ca
• These particles carry a property (like mass)
  called electric-charge.
• Electric charge can be positive or negative
• Electric charge is a scalar It is a quantity
  independent of any direction in space (compare
  temperature vs. velocity)
• Positive attracts negative
• Positive repels positive, Negative repels
  negative
• Charge adds linearly put together charge q1 and
  charge q2, they act like q3 q1 q2.
• Charge is conserved 0 q (-q)

10
Insulators Conductors

• Charges placed on an insulator (plastic, wood,
  ceramic) stay putin spite of the electric forces
  on them
• Fnet0
• Binding force acts like a microscopic spring. As
  external electric force pulls on charge on
  insulator, the binding force pulls back (up to
  some limit spring breaks)
• Charges placed on a metal are free to move in
  response to electro-magnetic (or other forces)
  ma F

11
Electrical Charge

• All physical quantities must be measured as
  multiples of a standard
• Time is measured in multiples of the standard
  second (now defined by atomic physics phenomena)
• Distance is measured in multiples of the standard
  meter (now defined in reference to the speed of
  light times the second).
• Mass is measured in multiples of the standard
  kilogram, housed near Paris, France.
• The SI unit of electrical charge is the Coulomb
• The Coulomb (C ) is defined from magnetic
  phenomena (skip till later).

12
The Structure of an Atom
The atom consists of a positively charged
nucleus, orbited by negatively charged electrons.
The nucleus contains protons (positive) and
neutrons (neutral). The orbital lines are an
accurate description of the orbits of electrons
in a highly excited atom The fuzzy red blob is a
better representation of the electron wave in the
atomic ground state (see Chap. 30).
13
The Electron

• One of the fundamental particles found in nature
  is the electron.
• The electron mass is 9.11 ? 10-31 kg.
• The electron charge (-e) is -1.6 ? 10-19 C.
• The symbol e is the magnitude of the electrons
  charge
• The electron is part of a family of fundamental
  particles known as leptons.
• Electron lifetime gt 1023 years (test of charge
  conservation). Eur. Phys. J. C 3, 1 (1998)

14
The Proton

• The proton is not a fundamental particle. It has
  a finite size (10-15 m) and a spectrum of excited
  states. It is understood to consist of three
  quarks bound together by a cloud of gluons and
  quarkanti-quark pairs.
• The proton mass is 1.67 ? 10-27 kg.
• The proton is 2000 times heavier than the
  electron, so the vast majority of an atoms mass
  resides in the nucleus.
• The proton charge (e) is 1.6 ? 10-19 C.
• The proton charge and electron charge are known
  to be equal and opposite to very high precision.
• qp qe/e lt 10-21 Eur. Phys. J. C 3, 1 (1998)

15

• An object may contain both positive and negative
  charges. If the object possesses a net charge it
  is said to be charged. If the object possesses
  no net charge it is said to be neutral.
• An atom is normally neutral, because it possesses
  an equal number of electrons and protons.
  However, if one or more electrons are removed
  from or added to an atom, an ion is formed, which
  is charged.
• Charge is always conserved charge may be
  transferred but it is never created or destroyed.
  
• However, charges can be created and destroyed in
  positive and negative pairs, so that the net
  charge in the universe does not change.

16
Electrical Forces

• Two charged objects will exert forces on one
  another.
• Unlike charges attract one another.
• Like charges repel one another.
• The force decreases with the square of the
  distance between the charges

17
Polarization
An object is polarized when its charges are
rearranged so that there is a net charge
separation. Charged objects can be attracted to
neutral objects because of polarization.
charged
neutral polarized
18
Insulators and Conductors

• Materials are classified by how easily charged
  particles can flow through them.
• If charges flow freely, the material is a
  conductor (metals, for example)
• If charges are unable to move freely, the
  material is an insulator (glass, for example)
• Some materials have properties in between
  insulators and conductors, these are called
  semiconductors.

19
Charge Transfer

• Charge is usually transferred because electrons
  move from one place to another.
• But sometimes the flow of both positively or
  negatively charged ions (atoms or molecules) is
  important (cells, batteries).
• The earth can be viewed as an infinite
  (conducting) reservoir of electrons. An object
  in electrical contact with the earth is said to
  be grounded.
• What happens when I ground the Van de Graaff
  generator? And why do I do this before touching
  the generator?

20
Properties of the Mutual Electrical Forces Acting
on Two Charges

• Each of the two charged object experiences a
  force that is equal and opposite to the force
  experienced by the other charge (Newtons Third
  Law).
• The force is attractive if the charges are unlike
  and repulsive if the charges are like.
• The force is inversely proportional to the square
  of the separation of the two charges, and is
  directed along the line joining them (attractive
  or repulsive).
• The force is proportional to the product of the
  magnitudes of the 2 charges.
• Remember force is a vector!

21
Coulombs Law

• The magnitude of the force between two point
  objects separated by a distance r with charges q1
  and q2 is given by Coulombs Law
• where k 8.99 ? 109 N?m2/C2 , precision of 10-7
  is linked to measurement of electron charge.
• or spherical charge distributions, or any
  objects whose size is much less than the
  separation distance r
• The direction of the force on one charge is
  either toward (negative) or away (positive) from
  the other charge.

q1 and q2 are the values ( or -) of the two
charges
22
Force vector, magnitude, component

• Magnitude (strictly positive)

• Component along direction from q1 to q2 of Force
  from q1 acting on q2.
• If q1q2gt 0, force is repulsive (pushes q2 away
  from q1)
• If q1q2lt 0, force is attractive (pulls q2 towards
  q1)

r
q1
q2
23
Comments on Coulombs Law

• 1/r2 ? Charge is conserved, Gauss Law
• Deviations from 1/r2 are measured to be less than
  1 part in 1010 over distance scales from (10-10 m
  to 1.0 m)
• The force is linear in the value of each charge.
• If an amount of charge 0.2q1 is brought from far
  away and added to q1, the force on q2 is
  increased to
• Why k? (Why not k1?)
• In Gaussian (or cgs) units, 1.00 esu is defined
  such that
• Two charges of 1.00 esu each separated by 1cm
  exert mutual forces on each other of 1 dyne 1
  gm cm2/sec2
• k 8.99 ? 109 N?m2/C2 1.00 dyne ?(cm)2/esu2.
• The value of k depends upon our choice of units
  for Force, Distance and Charge.

24
Subscript labels on Force
25
Vectors and Scalars

• A scalar is a physical quantity with magnitude,
  but without direction in space.
• Temperature
• Mass
• Energy, Time, Charge
• A Vector is a physical quantity with magnitude
  and direction in space.
• Displacement
• Momentum
• Velocity, Force

26
Vector Components Unit Vectors

• A vector can be expressed in terms of a
  coordinate system.
• Force vector
• F 1.6 N oriented 110 counter-clockwise from
  x-axis.
• Force Vector
• F (1.6 N)(cos110) along x-axis plus
  (1.6N)(sin110) along y-axis

q110?
x
27
Walker Problem 13, pg. 641
Given that q 12 mC and d 16 cm, (a) find the
direction and magnitude of the net electrostatic
force exerted on the point charge q2 in Figure
19-30. (b) How would your answers to part (a)
change if the distance d were tripled?
28
Solution
Draw free body for JUST q2
29
Problem 13, Solution, contd

• B) Tripling the separations decreases all forces
  by a factor of 329
• F2 22.4 N, x direction

30
Relative Strength of Gravity and Electrostatics

• In the hydrogen atom, the electron and proton are
  separated by 0.510-10 m
• The ratio of gravitational attraction between the
  electron and proton divided by the electrostatic
  attraction is
• FG/FQ 10-39 (see text)
• This ratio is independent of the separation
• Both forces are 1/r2.
• Why is gravity so much more important in the
  solar system?

31
Multiple Charges

• If there are more than two charges present, the
  net force on any one charge is given by the
  vector sum of the forces on that charge from all
  surrounding charges. This is an example of the
  Principle of Superposition.

F

F-

What is the direction of the net force on each
charge (roughly)?
32
Walker (1st edition)Problem 19, pg. 641
(a) Find the direction and magnitude of the net
electrostatic force exerted on the point charge
q3 in the Figure. Let q 1.8 mC and d 22 cm.
(b) How would your answers to part (a) change if
the distance d were doubled?
33
Solution

• Force F3,2 on q3 from q2 is repulsive
• Force F3,1 on q3 from q1 is attractive
• Force F3,4 on q3 from q4 is repulsive
• Distance from q2 to q3 is d
• Distance from q4 to q3 is d
• Distance from q1 to q3 is (?2)d

34
Solution, contd
Add the force vectors graphically
F3,4
FNet
F3,2
F3,1
35
Solution, four charges
y
FNet

• Find angle q from x-axis
• Cosq FNet,x/ FNet
• Cosq (2.97N)/(7.22N)
• q 65.7?

q
x
36
Spherical Charge Distributions
In general a spherical charge distribution
behaves as if all of its charge were at the
center of the sphere. Use the distance to the
center of the sphere to calculate the
electrostatic force.
q2
q1
r
37
Newton Action at a DistanceFaraday Force
Fields

• A mass m exerts a gravitational force GmM/r2 on a
  second mass M separated by a distance r, and vice
  versa.
• Coulomb gave us the same picture for
  electrostatic forces
• Faraday offered a new insight, introducing the
  Electric Field, which can be thought of as
  carrying the force from charge q to charge Q.
• In physics, a field means a physical variable
  that has a defined value at every point in space.
  Examples
• Temperature map, Barometric Pressure map (a
  scalar field)
• Wind velocity map (a vector field)
• Initially just a mathematical trick, with our
  understanding of electromagnetic waves and the
  quantum nature of light, Electric and Magnetic
  fields are as real as charge and mass.

38
Electric Field

• If a test charge q0 experiences a force F at a
  given location r, the magnitude of the electric
  field at that location is defined by
• The electric field is a what if concept. What
  would be the electrostatic force acting on a
  charge q0 if it were placed at position r?
• The electric field can also be thought of as a
  disturbance in space caused by nearby charges.
• The electrostatic force experienced by a charge
  is the interaction between the charge and the
  electric field at that position.
• The SI units of electric field are
  Newtons/Coulomb N/C

39
Electric Force F(r) from charge Q acting on a
test charge q0 at various locations r (x,y,z)
FkQq0/r2 Electric Field E(r) F/ q0
q0
Q
40
Electric Field E(r) from charge Q at various
locations r EkQ/r2
r
Q
41
Electric Field

• A vector at every point in space that
  tells us the magnitude and direction of the force
  a charge q will experience
  if the charge q is placed at the position
  (x,y,z).
• If qlt0, then the force F on q is opposite E.
• To measure E F/q, q must be small enough that
  it doesnt change the distribution of charges
  that created the electric field in the first
  place.

42
Electric Field Direction

• The direction of the electric field is defined to
  be the direction of the force that would be
  experienced if the test charge is positive.
  Because the field has a direction, it must be a
  vector.

E
q0
q0
E

43
Electric Field (cont.)
The electric field is the force per charge at a
given location. If you know the electric field,
then the force on a charge can easily be found
using F qE
Example A charge q of 8 mC experiences a
uniform electric field of 1000 N/C to the right.
(a) What is the force on the charge? (b) What
would the force be if the charge were 8 mC?
Note In problems like this we do not need to
know what charges created the electric field.
44
Electric Field of a Point Charge

• From Coulombs Law, the magnitude of the force
  experienced by a test charge q0 a distance r from
  a charge q is

Since the definition of the electric field is
the magnitude of the electric field from a point
charge is given by
45
Walker Problem 28, pg. 642
What is the magnitude of the electric field
produced by a charge of magnitude 10.0 mC at a
distance of (a) 1.00 m and (b) 2.00 m?
k 8.99 109 N m2/C2
46
Electric Field Polarization

• What is the magnitude of an electric field strong
  enough to polarize the molecules in the air to
  the point that electrons are pulled out of the
  air (ionization produces a spark)?
• Several Million Newton/Coulomb.
• Several Million Volt/meter

47
Electric Fields in Nuclear Physics

• What is the electric field at the surface of a
  proton?
• (radius 10-15 m, charge 1.610-19 C)
• E (8.99 109 N m2/C2)(1.610-19 C)/(10-15 m) 2
• E(14.4) 109-1930 N/C
• E1.44 1019 N/C
• Thats big!

48
Electric Fields in Atomic/Molecular physics

• What is the electric field from the hydrogen
  nucleus (proton) at a distance of one atomic
  radius (r0.5Å0.510-10m)
• E k q / r2
• E (8.99 109 N m2/C2)(1.610-19 C)/(0.510-10
  m) 2
• E (58)(109-1920) ( N/C)
• E 5.8 1011 N/C
• Smaller, but still very large.

49
Superposition
Just like with forces, electric fields must be
added as vectors. The electric field from
several charges is the vector sum of the electric
field from each charge.
Example Consider two identical negative charges
as shown. At which lettered point is the
magnitude of the electric field greatest? Least?
c
a
d
b
50
Superposition
E2
E1
E
-
-
Q2 Q1
Q1lt0
E2
E
E1
51
Walker Problem 66, pg. 644
An object of mass m 3.7 g and charge q 44 mC
is attached to a string and placed in a uniform
electric field that is inclined at an angle of
30.0 with the horizontal. The object is in
static equilibrium when the string is horizontal.
Find (a) the magnitude of the electric field and
(b) the tension in the string.
52
Walker Problem 66, pg. 644
qE
T

• Free Body Diagram
• Net force 0
• S Fx0 qEsin30o mg 0
• m 3.7E-3 kg, q 44.E-6 C
• E mg/(q sin30o) (3.7E-3 kg)(9.8m/s2)/(0.544.
  E-6 C)
• E 1.65E3 (kgm/s2)/C 1.65E3 N/C
• S Fy0 qEcos30o T 0
• T (44.E-6 C) (1.65E3 N/C)0.866 6.3E-2 N

mg
53
Electric Field Lines

• In order to visualize the electric field in space
  it is convenient to draw Electric field-lines
  (see Fig. 19-13). The field lines are
  directional curved lines that everywhere point
  in the direction of the electric field at that
  point.

Dipole
54
Field Line Properties

• The electric field is tangent to the field line
  at any point in space.
• The strength of the electric field is
  proportional to the density of field lines (areal
  density measured perpendicular to field line).
• The field lines always begin on positive charges
  or at infinity and end on negative charges or at
  infinity.
• No two field lines can ever cross.
• The number of field lines leaving a positive
  charge or approaching a negative charge is
  proportional to the magnitude of the charge.

55
Electric Field Lines
Note that twice as many field lines originate
from the 2q charge than the q or q charges.
56
Lecture 2, Quiz 1

• 1. The net charge inside the green blob is
• Positive
• Zero
• Negative
• Hint Are there more Electric Field lines
  entering, or leaving the blob, or is it equal?

57
Lecture 2, Quiz 2

• 2. The net charge inside the green blob is
• Positive
• Zero
• Negative
• Hint Are there more Electric Field lines
  entering, or leaving the blob, or is it equal?

58
Lecture 2, Quiz 3

• 3. The net charge inside the green blob is
• Positive
• Zero
• Negative
• Hint Are there more Electric Field lines
  entering, or leaving the blob, or is it equal?

59
Walker Problem 37, pg. 642
The electric field lines surrounding three
charges are shown in the Figure. The center
charge is q2 -10.0 mC. (a) What are the signs
of q1 and q3? (b) Find q1. (c) Find q3.
60
Parallel-Plate Capacitor
Two parallel conducting plates with opposite
charge, separated by a distance d, is known as a
parallel-plate capacitor. The electric field is
uniform between the plates (except near the
edges, not shown). Uniform means the electric
field magnitude and direction are the same
everywhere (in gap). This is because of, not in
spite of Coulombs 1/r2 law!!
61
Electrostatic Equilibrium

• Recall that charges within a conductor are free
  to move around easily.
• If the charges within a conductor are not in
  motion, then the system is said to be in
  electrostatic equilibrium.

62
Properties of Electrostatic Equilibrium

• In the presence of electrostatic forces, the
  charges on the conductor move around until the
  following static conditions are achieved
• The electric field is zero everywhere inside a
  conductor.
• The excess charge on a conductor resides entirely
  on its surfaces.
• The electric field just outside a charged
  conductor is perpendicular to its surface.
• On irregularly shaped objects, the charge
  accumulates at sharp points, and the electric
  field is most intense at sharp points.

63
Electric Flux
We define electric flux F as the product of the
surface area A times the component Ecosq of the
electric field perpendicular to the surface. In
general, F EAcosq. (a) F EA (b) F 0 (c) F
EAcosq
q is the angle between the electric field and the
line perpendicular to the surface.
64
Gausss Law
Consider an arbitrary (imaginary) closed surface
(called a Gaussian surface) enclosing a total
charge q. The electric flux through the surface
is
This integral property is a consequence of the
1/r2 Coulomb Law, and is valid for any irregular
surface, no matter how complicated the electric
field produced by internal or external charges.
65
Example
Three point charges are arranged as shown. q1
4 mC, q2 -6 mC and q3 -4 mC. Find the
electric flux through the three Gaussian surfaces
labeled a, b and c.
b
c
q1
a
q3
q2
66
Walker Problem 49, pg. 643
A thin wire of infinite extent has a charge per
unit length of l. Using the cylindrical Gaussian
surface shown in the Figure, show that the
electric field produced by this wire at a radial
distance r has a magnitude given by
67
Walker Problem 49, pg. 643solution
By symmetry, Electric force on a test charge is
directed radially outward (if lgt0). Closed
Gaussian surface consists of the cylinder and its
two end caps. Electric flux through end caps is
zero because E is parallel to surface. Electric
flux through cylinder wall FArea E(r ) F
2p r L E(r ) Net Flux 0 0 2p r L E(r )
(charge enclosed)/e0 L l /e0
68
Charges on (and in) a conductor

• Charge on a conductor is free to move under the
  influence of its mutual repulsion.
• Are the charges in a) or b) farther apart?
• The quantitative meaning to this question is
  Which configuration gives the lowest value for
  the electrostatic energy? (See Chap 20.)
• It is a property of the 1/r2 law (not just
  repulsion) that all the excess charge on a
  conductor ends up on the SURFACE.
• This can be an inside, as well as outside
  surface!!

69
Quiz 1Jan 10, 2005

• Two charges Q1 and Q2 are separated by a distance
  of 0.010 m. The Electrostatic force of Q1 on Q2
  is 2.0e-5 N.
• At what distance of separation between Q1 and Q2
  would the force be 1.0e-5N?
• a) 0.02 m b) 0.014 m c) 0.01 m
• d) 0.007m e) 0.005 m

70
Quiz 112 January 2004
Name

• In the diagram at right, F1 is the electrostatic
  force of Q1 acting on charge q1.0E-9C .
• Draw a vector with its tail at q to represent the
  magnitude and direction of the electrostatic
  force F2 of Q2 acting on charge q (the length of
  your vector should roughly describe the relative
  magnitudes of F2 and F1.
• Draw a vector with its tail at q to represent the
  magnitude and direction of the net force FNet
  acting on q from both Q1 and Q2
• Label your vectors F1 and FNet
• Note

Q1 1.0E-6 C
q
F1
Q2 -1.0E-6 C
71
Quiz 22 February 2004
Sketch the electric field lines generated by
these two charges. Hint Consider the electric
flux through the three gaussian surfaces defined
by the three dashed lines.
Name
4mC
-2mC
72
Preparation for Lab 2 (Chapter 21)

• Electric Current in wire equals steady flow of
  charge (not equilibrium!).
• Unit of measure is Coulomb per second Amp
• 1.00 C/s 1.0 A
• Think of electric current like flow of water in
  pipe.
• Voltage Electrostatic Potential difference of
  power supply or battery (e.g. AA1.5 V)
• How hard the current is being forced around
  circuit.
• Think of difference in height of two ends of a
  water pipe. Water flows with greater force when
  the height difference is greater.
• Resistance R measure of how hard you have to
  push to obtain current (flow). R V/I
• Think of long thin pipe (high resistance to flow)
  versus short broad pipe (low resistance to flow).

Pump
73
Equivalence of Gauss Law and Coulombs Law

• Coulomb Electric field at a distance r from a
  point charge Q
• E(r) k Q / r2 Q / (4p e0 r2)
• For Qgt0, Egt0 E points away from Q
• For Qlt0, Elt0 E points towards Q.
• Gauss Electric flux through an imaginary closed
  spherical shell a distance r from Q
• Flux E(r)(Surface area of shell) E(r) 4p r2
• Outward flux is positive
• Inward flux is negative
• Gauss Flux Q/ e0.
• E(r) Q / (4p e0 r2)

E
Q
r
74
Gauss Law and the Parallel Plate Capacitor

• Consider a rectangular Gaussian surface
  penetrating into the metal of a parallel plate
  capacitor
• Total Charge on left plate Q, right plate -Q
• Total area or each plate A
• Surface charge density s Q/A
• Surface area of face of Gaussian surface parallel
  to plate a.
• Charge enclosed by Gaussian surface sa
• Flux through portion of Gaussian surface inside
  metal 0 (E0).
• Flux through top and bottom surfaces outside
  metal 0 (Electric field parallel to surface).
• Flux through face of Gaussian surface parallel to
  plate (outside) Ea.
• Gauss Law sa/e0 Ea
• Uniform Electric Field in gap E s/e0

- - - - - - - - - - -

a