20. Electric Charge, Force, and Field

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20. Electric Charge, Force, and Field
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Topics

• Electric Charge
• Coulombs Law
• Electric Field
• Electric Dipole Moment

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Electric Charge
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The Triboelectric Effect

• Air Most Positive
• Human skin
• Rabbit fur
• Glass
• Silk
• Paper
• Cotton/Steel
• Wood
• Rubber balloon
• Silicone rubber Most Negative

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Glass rods rubbed with silk
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Glass rod rubbed with silk vs. rubber rod rubbed
with fur
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The Unit of Charge

• The SI unit of charge is the coulomb (C)
• 1 coulomb is about 6.25 x 1018 elementary
• charges
• Therefore, one elementary charge is about
• e 1.60 x 10-19 C

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Coulombs Law
Charles Augustin de Coulomb (1736 1806)
Wikemedia Commons
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Coulombs Law
Force of charge q1 on q2
k 9.0 x 109 Nm2/C2
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Superposition Principle

• Coulombs law is valid for point charges that
  is, charged objects of negligible size.
• Luckily, however, we live in a universe in which
  the electric force is additive the force on a
  point charge, due to other charges, is simply the
  sum of all the (two-body) electric forces.
• The electric force obeys the superposition
  principle.

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Superposition Principle
What is the net force on charge q0? It is the
sum of the two-body forces F1,0 and F2,0.
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The Electric Field
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The Electric Field
q1
q2
Force of charge q1 on q2
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The net force on charge q0 is sum of forces due
to charges q1 and q2
Force of q1 on q0
q0

Force of q2 on q0
q1
q2

-
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The Electric Field
q0
The expression

suggests the concept of the electric field of a
point charge where is the unit
vector away from the charge
q.
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The Electric Field
A field line shows the direction of the
electric force on a positive point charge
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The electric field at a given point P is the sum
of the electric fields due to every point charge
P
-


-
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A charge distribution
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If the charge distribution can be approximated as
a continuous distribution, we can replace the sum
by an integral
See Examples 20.6 20.7
P
-


-
-


A charge distribution
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The Electric Field
The electric force on a charge q is
which, together with Newtons 2nd Law,
can be used to calculate the motion of an
electric charge, of mass m
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Electric Field
Newtons 2nd Law for an electric charge can be
written as
If E is constant, both in direction and
magnitude, so to is the acceleration of the
charge.
Note that the acceleration depends on the charge
to mass ratio.
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The Electric Dipole
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The Electric Dipole
a
a
P
-q
q
x
The electric field at point P far away is
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The Electric Dipole
a
a
P
-q
q
x
Dipoles are so common in Nature that
physicists have found it useful to define a
quantity called the electric dipole moment
d is a vector of length 2a, from q to q
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Dipoles in Electric Fields
The ve charge wants to move right, while the
ve charge wants to move left
The net torque on the dipole is the sum of the
torques due to forces F- and F. It can be
written as
The potential energy of the dipole is
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Example H2O
The water molecule has an electric dipole
moment of magnitude 6.2 x 10-30 Cm 40 epm
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Conductors, Insulators, and Dielectrics
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Conductors, Insulators, and Dielectrics

• Matter contains huge numbers of point charges.
  For example, a typical glass of water contains on
  the order of 1025 protons and 1025 electrons!
• In materials called conductors, some of these
  charges are free to move, while in insulators
  charges are not free to move.

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Conductors, Insulators, and Dielectrics

• Some molecules, like H2O, have permanent dipole
  moments. Others can be distorted by an electric
  field, and become dipolar that is, acquire
  induced dipole moments. These materials are
  called dielectrics

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Summary

• Electric charge
• The force between two point charges obeys
  Coulombs law F k q1 q2 /r2
• Electric field
• This is the force per unit charge at a point
• Electric force is given by F qE
• Electric dipole
• Experiences a torque in a uniform electric field.