Physics 2220

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Physics 2220

• Physics for Scientists and Engineers II

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Chapter 23 Electric Fields

• Materials can be electrically charged.
• Two types of charges exist Positive and
  Negative.
• Objects that are charged either have a net
  positive or a net negative charge residing on
  them.
• Two objects with like charges (both positively or
  both negatively charged) repel each other.
• Two objects with unlike charges (one positively
  and the other negatively charged) attract each
  other.
• Electrical charge is quantized (occurs in integer
  multiples of a fundamental charge e).
• q ? N e (where N is an integer)
• electrons have a charge q - e
• protons have a charge q e
• neutrons have no charge

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Material Classification According to Electrical
Conductivity

• Electrical conductors Some electrons (the free
  electrons) can move easily through the material.
• Electrical insulators All electrons are bound to
  atoms and cannot move freely through the
  material.
• Semiconductors Electrical conductivity can be
  changed over several orders of magnitude by
  doping the material with small quantities of
  certain atoms, making them more or less like
  conductors/insulators.

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Shifting Charges in a Conductor by Induction
uncharged metal sphere

Negatively charged rod
Left side of metal sphere more positively charged
Right side of metal sphere more negatively charged
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Coulombs Law (Charles Coulomb 1736-1806)

• Magnitude of force between two point charges q1
  and q2 .

Coulomb constant
r distance between point charges
Permittivity of free space
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Charge

• Unit of charge Coulomb
• Smallest unit of free charge e 1.602 18 x
  10-19 C
• Charge of an electron qelectron - e - 1.602
  18 x 10-19 C

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Vector Form of Coulombs Law

• Force is a vector quantity (has magnitude and
  direction).

unit vector pointing from charge q1 to charge q2
Force exerted by charge q1 on charge q2 (force
experienced by charge q2 ).
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Vector Form of Coulombs Law

• Force is a vector quantity (has magnitude and
  direction).

unit vector pointing from charge q2 to charge q1
Force exerted by charge q2 on charge q1 (force
experienced by charge q1 ).
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Directions of forces and unit vectors
q2
-
q2
q1
q1
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Calculating the Resultant Forces on Charge q1 in
a Configuration of 3 charges
a 1cm
q1
q2
0.5 cm
0.5 cm
q3
-
q3 - 2.0 mC
q1 q2 2.0 mC
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Forces acting on q1
q3
Total force on q1
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Magnitude of the Various Forces on q1
Note I am temporarily carrying along extra
significant digits in these intermediate results
to avoid rounding errors in the final result.
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Adding the Vectors Using a Coordinate System
y
q3
x
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Adding the Vectors Using a Coordinate System
y
x
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doing the algebra
F1 has a magnitude of
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Calculating the force on q2 another example
using an even more mathematical approach
Charges
Location of charges
q1 3.0 mC
x13.0cm y12.0cm z15.0cm
q2 - 4.0 mC
x22.0cm y26.0cm z22.0cm
In this example, the location of the charges and
the distance between the charges are harder to
visualize ? Use a more mathematical approach!
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Calculating the force on q2 another example
using an even more mathematical approach
d12distance between q1 and q2.
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Calculating the force on q2 mathematical
approach
We need the distance between the charges. d12
is distance between q1 and q2.
y
q1
q2
x
z
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Calculating the force on q2 mathematical
approach
Distance between charges q1 and q2 .
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Calculating the force on q2 mathematical
approach
We need the unit vectors between charges. For
example, the unit vector pointing from q1 to q2
is easily obtained by normalizing the vector
pointing from from q1 to q2.
y
q1
q2
x
z
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Calculating the force on q2 mathematical
approach
The needed unit vector
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Calculating the force on q2 mathematical
approach
You can easily verify that the length of the unit
vector is 1.
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Calculating the force on q2 another example
using an even more mathematical approach
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Calculating the force on q2 another example
using an even more mathematical approach
and if you want to know just the magnitude of
the force on q2
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23.4 The Electric Field
It is convenient to use positive test charges.
Then, the direction of the electric force on the
test charge is the same as that of the
field vector. Confusion is avoided.
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23.4 The Electric Field
Q
qo



test charge


Source charge
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23.4 The Electric Field
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23.4 The Electric Field of a Point Charge q
q0
r
q
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23.4 The Electric Field of a Positive Point
Charge q
(Assuming positive test charge q0)
q0

Force on test charge
P

Electric field where test charge used to be (at
point P).
The electric field of a positive point charge
points away from it.
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23.4 The Electric Field of a Negative Point
Charge q
(Assuming positive test charge q0)
q0
-
Force on test charge
P
-
Electric field where test charge used to be (at
point P).
The electric field of a negative point charge
points towards it.
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23.4 The Electric Field of a Collection of Point
Charges
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23.4 The Electric Field of Two Point Charges at
Point P
y
P
y
q1
q2
x
a
b
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23.4 The Electric Field of Two Point Charges at
Point P
y
P
Pythagoras
r2
r1
y
x
a
b
q1
q2
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23.4 The Electric Field of Two Point Charges at
Point P
y
P
x
q1
q2
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23.4 The Electric Field of Two Point Charges at
Point P
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23.4 The Electric Field of Two Point Charges at
Point P
Special case q1 q and q2 -q AND b a
E from charge
E from - charge
-

q
-q
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23.4 The Electric Field of Two Point Charges at
Point P
Special case q1 q and q2 q AND b a
E from other charge
E from charge


q
q
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This is called an electric DIPOLE
Special case q1 q and q2 -q AND b a
E from charge
E from - charge
-

q
-q
For large distances y (far away from the dipole),
y gtgt a
E falls off proportional to 1/y3 Fall of faster
than field of single charge (only prop. to
1/r2). From a distance the two opposite charges
look like they are almost at the same place and
neutralize each other.