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Monday, January 5, 2009

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Title: Monday, January 5, 2009


1
Monday, January 5, 2009
  • Spherical Distribution Laws

2
Announcements
  • USAYPT participantsI need paperwork and fees by
    tomorrow at the latest!
  • New notes packetwere starting EM!

3
When we say that an object is charged, what do
we really mean?
  • If a particle bears an electrical charge, we can
    generally assume it has an excess of electrons
    (negative charge) or an excess of protons
    (positive charge).
  • Fine point usually, only electrons move, so
    positive charge (an excess of protons) is really
    an absence of electrons.

4
Fundamentals of Electrical Charge
  • Charge on electron -e
  • Charge on proton e
  • e 1.602 ? 10-19 Coulombs , C
  • Any charge q is a multiple of the number of extra
    electrons or missing electrons such that q ne

5
Lets talk about spherical distribution.
  • What do you think we mean by a spherical
    distribution law? Give an examples.

6
Lets talk about spherical distribution.
  • Write the formula for the surface area of a
    sphere.

7
Spherical distribution law for gravity
Newtons Law of Gravity
G 6.7 ? 10-11 Nm2/kg2 m1 and m2 are spherical
or point masses in kg. r is the separation
between the centers of the masses
8
Spherical distribution law for electrical force
  • k 8.99 ? 109 Nm2/C2
  • q1 and q2 are spherical or point charges in
    Coulombs.
  • r is the separation between the centers of the
    charges

Coulombs Law
9
How are electrical and gravitational forces
similar?
  • They both follow spherical distribution laws. The
    forces diminish as the surface area of a sphere.

10
How are electrical and gravitational forces
different?
  • Electrical forces can be attractive or repulsive,
    while gravitational forces are only attractive.
  • Gravitational forces are much weaker than
    electrical forces.

11
For Two Charges
  • The electrostatic force is repulsive if the
    charges are of the same sign and attractive if
    the charges are of unlike sign.
  • The force exerted on charge A by charge B is
    always equal and opposite of the force exerted by
    charge B on charge A (Newtons 3rd Law)

12
For More Than Two Charges
  • Determine the force on a charge due to each of
    the other charges in the vicinity.
  • Do a vector addition.

When you are determining electrostatic force, you
focus on one charge.
q
Its all about me! Who is nearby who can affect
me?
13
Sample problem Using unit vector notation, write
an expression for the force exerted on the upper
right charge by the other two charges.
5.0 mC
-2.0 mC
-

0.10 m
0.10 m

5.0 mC
14
Tuesday, January 6, 2009
  • Gravitational and Electric Fields

15
Announcements
  • USAYPT participantsI need paperwork and fees
    today.

16
Sample problem Two identical balls of mass m and
charge q are hanging from strings of length L.
Derive an expression for q in terms of m, ?, L,
and fundamental constants.
?
L
L
m,q
m,q
17
What is meant by a force field?
  • A force field creates a force when an object is
    placed in it. It is a property of empty space.
  • An electric field creates an electric force on a
    charge placed in it.
  • The electric field is created by a charge
    distribution.
  • A gravitational field creates a gravitational
    force on a mass placed in it.
  • The gravitational field is created by a mass
    distribution.

18
Gravitational Field
  • Draw the gravitational field around the earth.

19
Gravitational Field
  • How can you calculate the gravitational force on
    a small mass in a gravitational field?

20
Gravitational Field
  • What is an equation that can be used for
    gravitational field calculations?

21
Gravitational Field
  • What is the value of the gravitational field at
    the surface of the earth?

22
And nowthe Electric Field
  • Boot up computer.
  • Go to my folder on the N drive
  • Go to Period 2, Projects, Volume 2
  • When you are at the right place, look up.

23
The Electric Field
  • Draw the electric field around a positive charge.

24
The Electric Field
  • Draw the electric field around a negative charge.

25
The Electric Field
  • How can you calculate the electric force on a
    small charge in an electric field from the
    magnitude of the electric field?

26
The Electric Field
  • What is an equation that can be used for electric
    field calculations?
  • What is the limitation of the equation shown
    above?

27
Summary of the Electric Field
  • This equation can be used to calculate the
    electric field a distance r away from a the
    center of a spherically symmetric charge
    distribution of qo Coulombs.
  • Another charge q entering the electric field
    created by qo will experience a force F, which
    can be calculated by the equation F qE.

28
Summary of Electric Field Direction
  • The direction of the electric field at a point in
    space is the direction that a small positive
    charge at rest (a test charge) wishes to move
    if it is placed at that location.
  • Thus, the electric field points away from
    positive charges and toward negative charges.
  • If more than one charges is generating the field,
    vector addition must be done to add the fields
    produced by each of the charges to get the
    resulting field. This is called superposition
    of the individual fields.

29
Wednesday, January 7, 2008
  • Charge distributions

30
Announcements
  • Saturday practice for USAYPT from 1000 to 200
    PM. Who can come?
  • Get out homework Ch23 7,8,9 for self correction.

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34
  • Sample problem Determine where the electric
    field is zero if a 2.0 mC charge is located at
    the origin and a -3.0 mC charge is located at x
    1.0 meter.

35
Limitations of Coulombs Law
  • Coulombs Law equations for Force and Field can
    only be used directly for point charges or
    spherically symmetric charges.
  • For more complicated continuous charge
    distributions we need to break up the charge
    distribution into little bitty pieces and use
    Coulombs Law and superposition together to
    determine the electric field at a given location
    in space near the charge distribution.

36
Linear Charge Distribution
  • When charge resides on a long thin object such as
    a wire or a ring, we call that a linear charge
    distribution.
  • It is sometimes convenient for us to define a
    linear charge density, ?, which is charge per
    unit length.
  • ? Q/L dQ/dL


















37
Surface Charge Distribution
  • When charge resides on larger surface, we call it
    a surface charge distribution.
  • It is sometimes convenient for us to define a
    surface charge density, s, which is charge per
    unit area.
  • s Q/A dQ/dA

























































38
General Procedure - continued
  • You need to integrate over a spatial variable
    (not charge!). Appropriate choices are linear
    distance, arc length, or angle (x,y,s,q,f)
  • Find a common variable that r and/or dq both
    depend on.
  • See if symmetry (and trig) can be used to
    simplify the problem by elimination of off-axis
    components of E.
  • Find the appropriate limits to the integral.
  • Dont skip set-up steps. The physics is in the
    setup!

39
Volume Charge Distribution
  • When charge resides distributed within a solid
    object, we have a volume charge distribution.
  • It is sometimes convenient for us to define a
    surface charge density, r, which is charge per
    unit area.

40
General Procedure for Electric Field Calculations
  • Each little infinitesimally small charge dq in a
    charge distribution containing Q total Coulombs
    creates its own tiny electric field dE at a point
    P in space a distance r from dq.
  • I can add all these little infinitesimal fields
    dE together to get the field at point P.
  • What does this sound like to you?

41
Thursday, January 8, 2008
  • More on Charge Distributions

42
Announcements
  • Get out HW Ch 23 13,14,15 to grade.

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45
Sample Problem
  • Determine the electric field magnitude and
    direction a distance y away from an extremely
    long, straight wire of charge density l.













































y
46
Sample Problem
  • Determine the electric field magnitude and
    direction a distance x away from a ring of radius
    R bearing charge Q.

x
R
47
Friday, January 9, 2009
  • Motion of Charged Particle in E-field

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50
  • Sample Problem Determine the electric field
    magnitude and direction at point P in the figure
    shown. The semicircular ring bears charge -2.0mC
    and has a radius of 0.50 m.

P
R
51
Motion of Charged Particles in Electric Fields
  • If the electric field is constant, acceleration
    will be constant, and kinematic equations can be
    employed.
  • The motion is not unlike projectile motion.

52
Sample problem
  • What is the speed and position of an electron
    released from rest in this electric field after
    3.0 ns?

e-
E 320 N/C
53
Sample problem
  • What is the velocity and position of this
    electron 3.0 ns after it enters the field?

E 320 N/C
y
e-
x
v 20,000 m/s
54
Static Electricity Experiment 1
  • Blow up the balloon and charge it by rubbing it
    against your hair. Can you deflect a flowing
    stream of water with the charged balloon?
  • Is the water charged? If not, why is it being
    deflected? See if your group can come up with a
    plausible answer.

55
Static Electricity Experiment 2
  • Cut 2 20-cm strips of transparent tape (mass of
    each 65 mg). Fold about 1 cm tape over at one end
    of each strip to create a handle. Press both
    pieces of tape side-by-side on your lab table and
    rub your finger back and forth across the strips.
    Quickly pull the strips off the lab table. Hold
    the handles together and the strips will repel
    each other, forming an inverted V. Estimate the
    charge on each strip. Assume the charges act as
    though they are at the center of mass of the
    strip.
  • Hint Begin by drawing a Free Body Diagram!

56
Monday, January 12, 2009
  • Electric Flux

57
Announcements
  • Get out homework (page 7 in packet)

58
Flux
  • Flux means flow.
  • Consider three rectangular wire loops in a vector
    field.
  • Which one has maximum flux (or flow) of the field
    lines through it?

max flux no flux intermediate
flux
59
To Increase Flux
  • Increase the field
  • Increase the area of the loop
  • Make sure the hoop is appropriately angled

max flux no flux intermediate
flux
60
The Area Vector
  • The area vector is defined as a vector
    perpendicular to a surface with magnitude equal
    to the scalar area of the surface.
  • Consider the angle between v and A.

A
A
A
For what angle is the flux maximum?
61
Flux Equation
  • The flux is proportional to field vector
    magnitude, area vector magnitude, and the cosine
    of the angle between them.

A
A
A
What vector operation does this sound like?
62
Flux Equation
A
A
A
What vector operation does this sound like?
63
Flux Equation for Electric Field
Units Nm2/C
A
A
A
64
Area Vectors For a Closed Shape
  • This rectangular prism has six surfaces. Each
    surface has an area vector that points outward
    from center of the prism, and is normal to the
    surface.

65
Another Example
  • This cylinder is a bit more complicated. The top
    and bottom have areas that can easily be
    calculated, and the corresponding vectors point
    outward. On the sides, we must define and
    infinite number of infinitesimally small areas,
    each of which defines a little vector (dA) that
    points outward.

66
The Calculation of Flux Over a Closed Surface in
a Vector Field
  • At each point on the closed surface, we must take
    the dot product with the vector field to get the
    flux for that small area. Then we add all these
    dot products up together to get the flux for the
    entire surface. This leads to some interesting
    observations.
  • If there is a source of the vector field in the
    closed shape, the flux over its surface is
    positive.
  • If there is a sink of the vector field in the
    closed shape, the flux over its surface is
    negative.
  • If there is neither a source or sink of the
    vector field in the closed shape, the flux over
    its surface is zero.

67
What do we mean by source and sink of an
electric field?
  • The source is where the field starts, and the
    sink is where the field terminates.
  • In an electric field, the source is the positive
    charge, and the sink is the negative charge.
  • Therefore,
  • If a closed shape encloses a positive charge, the
    flux is positive.
  • If a closed shape encloses a negative charge, the
    flux is negative.
  • If the closed shape encloses no net charge, the
    flux is zero.

68
Mathematical Representation
  • For a general vector field, v
  • For an electric field, E

In an electric field, the closed shape we
integrate the flux over is referred to as a
Gaussian surface.
69
  • Sample Problem Calculate the electric flux
    through a spherical surface of radius 2.0 m
    containing a point charge of 3mC at its center.

70
  • Problem 24.1 Draw an electric dipole, and sketch
    three Gaussian surfaces for which one has
    positive electric flux, one has negative electric
    flux, and one has zero electric flux.

71
  • Problem 24.2 A vertical field of 2.4 x 104 N/C
    exists above Earths surface when thunderstorm is
    brewing. What is flux through car of approximate
    rectangular size of 5.0 m by 3.0 m if it is
    traveling on a road with a 10o slope.

72
  • Problem 24.6 A uniform field of ai bj
    intersects a surface of area A. What is the flux
    through the area if the surface lies in (a) the
    xy plane? (b) the xz plane (c) the xy plane?

73
  • Problem 24.9 A cone with base radius R and
    height h is located on a horizontal table. A
    horizontal uniform field E penetrates the cone.
    Determine the electric flux that enters the
    left-hand side of the cone.

74
Tuesday, January 13, 2009
  • Gausss Law of Electricity

75
Announcements
  • Get out homework Problems 23 46,47,52

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79
Gauss Law of Electricity
  • q net charge (C) enclosed inside a given
    Gaussian surface. This is a sum of all and -
    charges
  • ?o electrical permittivity of free space
  • 8.85 ? 10-12F/m
  • 8.85 ? 10-12C2/Nm2
  • ?E electrical flux over the Gaussian surface

80
Other forms of Gausss Law
Integral forms give indication of enclosed charge.
Differential form gives indication charge
density. For more information see
http//hyperphysics.phy-astr.gsu.edu/hbase/electri
c/maxeq2.html
81
Gaussian Surface
  • A Gaussian surface is simply any closed shape in
    space, which can be of any arbitrary shape.
  • All Gaussian surfaces give the same answer in
    Gausss Law if they enclose the same net charge!
    So, to make the math easier, Gaussian surfaces
    are typically chosen for convenience and high
    symmetry with regard the electric field.

82
Whats Gausss Law Good For?
  • Gausss Law can be used to determine how much
    charge is enclosed in a surface.
  • More commonly, Gausss Law is used to determine
    the electric field at a point in space.

83
Sample Problem
A point charge q is located a distance d from a
long infinite wire. Determine the electric flux
through the plane due to the point charge.
84
Non-constant Fields
  • Do some investigating of the properties of
    electric fields at
  • http//www.falstad.com/mathphysics.html

85
January 14, 2009
  • Application of Gausss Law

86
Announcements
  • Get out HW problems 24 3,5,7,8
  • Exciting movie

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89
Sample Problem Consider two Gaussian surfaces, a
sphere of radius R and a cube of side 4R. In each
is a positive point charge of q. How does the
electric flux compare for the two surfaces?
90
  • Sample Problem Derive the electric field a
    distance y away from a long charged wire bearing
    a linear charge distribution l. (NOT IN PACKET)













































y
91
  • Sample Problem Derive the electric field outside
    a charged non-conducting cylinder with an even
    charge distribution.

92
  • Sample Problem Derive the electric field INSIDE
    a charged non-conducting cylinder with an even
    charge distribution.

93
January 15, 200 8
  • Electric Force Lab

94
Announcements
  • Problems 24 13,14,15
  • Movie!

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