Physics 2Ba

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Physics 2B(a)

• Electricity and Magnetism

Winter 2004
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George M. Fuller 427 SERF gfuller_at_ucsd.edu 822-1
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Office Hours 200 PM - 330 PM Tuesday 329 SERF
PM
TH 700 PM - 800 PM WLH 2204
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problem assignment TBA
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Charge, Coulombs Law, and Electric Field
Lectures 1, 2, 3
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The Forces of Nature
The Strong Force (which your book calls the
color force
because there are three charges red, green, and
blue). This is the force between
quarks and gluons that holds atomic
atomic nuclei together. The Electromagnetic
Force about 100 times weaker than the strong
force
two charges plus and minus. The Weak
Force about 20 orders of magnitude weaker than
electricity
responsible for nuclear beta decay, changes
neutrons to
protons and vice versa. This is how neutrinos
interact. Gravitation the weakest force by far!
About 39 orders of magnitude weaker
than electricity!
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Overview of Electromagnetism

• Greeks note that rubbing materials can cause them
  to attract/repel
• and they note that certain stones from Magnesia
  attract iron.
• 18th century parlor tricks
• Franklin figures out that there are two kinds of
  electric charge.
• 19th century Faraday performs revealing
  experiments
• Maxwell discovers
  equations which unify electricity and
• magnetism and lead
  to the prediction of electromagnetic
• waves and the
  development of Einsteins relativity.
• 20th century Relativity, the photoelectric
  effect, quantum mechanics,
• all lead to the
  development of quantum electrodynamics.
• Unification of the
  electromagnetic and weak interactions.
• 21st century ?

Technological Revolution
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Coulombs Law
Like charges repel, opposite charges attract net
electric charge is conserved. We will label the
two kinds of charge as either positive or
negative. Then the force between two point
charges is
the force exerted on charge q2 by the charge q1
unit vector points from q1 towards q2


-

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Coulombs Constant
Where the unit of charge that we will use is the
Coulomb
permittivity constant
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The Shocking Truth About Electricity
The electric force is phenomenally strong!
Consider a comparison between the electric and
gravitational forces acting between the electron
and the proton in a hydrogen atom.
Gravitational Force
proton
Electric Force
electron
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Why then arent we painfully aware of electric
forces?
The answer has two parts (1.) In ordinary
materials, the positive and negative electric
charges balance (that is, they add up to
zero net charge) to extraordinary
precision. (2.) The electric force has a
remarkable property the superposition
property.
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Vectors in 2 Dimensions
If any of this looks unfamiliar you should
immediately review vector algebra/calculus.
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two-dimensional coordinates and vectors
y - axis
y
x - axis
x
unit vectors point along positive x and y axes
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inner (scalar) product of two vectors
Ay
By
Ax
Bx
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Example Problem 11, Chapter 23
A proton is on the x-axis at x 1.6 nm. An
electron is on the y-axis at y 0.85 nm. Find
the net force the two exert on a helium(He)
nucleus (charge 2e) at the origin.
Solution first draw a picture then guess the
answer then set up the algebra
then plug in the numbers with their
units/dimensions then cancel and re-work
the final units and make sure that
they make sense!
Vector force exerted by electron on He nucleus
y - axis
-e
2e
e
x - axis
Vector force exerted by proton on He nucleus
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Point Charges and the Superposition Principle
Electric forces simply add vectorially
If
you want the force on a point charge exerted by
other point charges, you simply add up the vector
forces from each individual charge


Example total force on charge Q
y-axis
y
x-axis
x a
x -a
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The Electric Field
Rather than find the force that a distribution of
charges exerts on a given (test) charge at a
particular point in space, it is convenient to
define the ELECTRIC FIELD at this point as the
force per unit (positive) charge
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What are the dimensions of Electric Field?
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Vectors in 3 Dimensions
A simple generalization of what we just did in
the examples in two dimensions!
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At a particular point in space x, y, z, the
(vector) force on a point particle with charge q
is
So, you can think of a vector residing at each
point in space. Of course, the vector will have
three components a scalar function Ex(x, y, z),
the component along the x-direction a scalar
function Ey(x, y, z), the component along the
y-direction a scalar function Ez(x, y, z), the
component along the z-direction.
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z-axis
z
y-axis
q
x
y
x-axis
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The radius vector from the origin to point (x, y,
z) is
Remember your vector algebra . . .
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inner (scalar) product of two vectors
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The Electric Field of a Point Charge
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The Electric Field of a Point Charge
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The Electric Field from a Distribution of Point
Charges
Again, simply use the superposition
principle. To find the Electric Field at a given
point in space, simply add up the contributions
from each individual charge. Calculate the
Electric Field contribution from each one of
these charges as if the other ones didnt exist.
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Example Electric Dipole
Two (point) charges of equal magnitude but
opposite sign at a fixed separation.
y-axis
y
x-axis
x a
x -a
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The Dipole Moment is defined to be the vector
with magnitude p q d that points from the
negative toward the positive charge.
z-axis
d
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Example Molecules can be
overall charge neutral but may
nevertheless possess an electric
dipole moment. The classic
example is the water molecule.
-
O
H
H


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Continuous Distributions of Charge
Of course, real materials are composed of
point-like electrons, protons, and neutrons. The
protons and electrons can be regarded, for our
purposes, as positive and negative point charges,
respectively. Any macroscopic object will
contain 1024 particles, however. In this
case we can approximate the distribution of
charge as continuous across the volume of
the object, given locally by a volume charge
density r (with dimensions Coulombs per unit
volume, or C/m3 ). Likewise, for charge spread
out over a surface, we can define a surface
charge density s (with dimensions Coulombs per
unit area, or C/m2 ). For charge spread out along
a line (e.g., an extremely thin wire) we can
define a line charge density l (with dimensions
Coulombs per unit length, or C/m). Then the
increment in charge associated with an increment
in volume, area, or length is
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With the charge in an object broken down into
particles or small increments dq, we can employ
the superposition principle to find the Electric
Field at any position.
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Example a uniformly charged ring of radius a
and charge Q. Find the
electric field on the axis through the ring.
Assume that the ring is very thin so that we can
regard the charge distribution on it as being a
line charge. Then the charge density (charge
per unit length)
is l Q/(2p a).
a
x
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Example continued . . .
Suppose the ring of radius 1 m carries a
uniformly distributed charge of 0.01 C. What is
the electric field a distance 8 m from the center
of the ring and along the center line?
Well this meets the conditions of what we had
just derived. We saw that the electric field
points along the center line and has magnitude
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Kinematics and Dynamics of Matter in Electric
Fields
For point particles of mass m and charge q in an
Electric Field E we have
For example, a uniform(constant in magnitude and
direction in some region of space) electric field
produces a constant acceleration of a particle.
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The Interaction of a Dipole with a uniform
Electric Field
q
-
d

The torque acts to try to line up the dipole
along the field.
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Calculate the work required to rotate a dipole
from a position orthogonal to the Electric Field
direction to a new angle q with respect to the
field orientation.
Associate this work with a change in a potential
energy which we can define as
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Conductors, Insulators, and Dielectrics
Materials in which (some) electrons are free to
move in response to an applied electric field we
term conductors. Insulators are materials where
charges are not free to flow as large
scale electric currents. However, the molecules
in insulators may be able to respond to an
applied electric field, for example, lining up
the intrinsic dipole moments of these molecules.
Molecules without intrinsic dipole moments may
acquire induced dipole moments in response to the
electric field. In either case, we call
these Substances dielectrics.