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Chapter 15
Electric Forces
and
Electric Fields
Chapter 15 Objectives
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Properties of electric charges
Conductor vs Insulator
Conduction vs Induction
Polarization
Coulomb’s Law
Electric field
Electric field lines
Electric flux
Gauss’ Law
Properties of Electric
Charge
• An electric charge is
positive because it
has lost electrons and
other negatively
charged particles.
– Represented by +
– Often drawn in red.
• An electric charge is
negative because it
has gained electrons
and other negatively
charged particles.
– Represent by –
– Often drawn in black.
This idea was first mentioned by Benjamin Franklin (1706-1790)
Behavior of Electric Charges
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Opposite charges attract one another.
– Like charges repel.
• Electric charge is conserved.
• The transfer of charge occurs because the negative
charge is transferred from one object to another.
– So objects either gain or lose negative charge.
• In order to become positive, an object will lose a negative charge.
• Robert Millikan (1886-1953) discovered that charges are
quantized, or said to have a fundamental unit of charge.
– Meaning the charge is full integer multiples
• + e, + 2e, + 3e, etc.
Conductor vs Insulator
• A conductor is a
material in which
electric charge moves
freely.
– Electrons are free to
move from atom to
atom.
• Metals are good
conductors.
• Water is a pretty good
conductor.
• An insulator is a material
in which electric charge
does not move freely.
– Electrons do not leave their
respective atoms
– Can maintain a charge,
but only at the surface
and it does not transfer
to other regions of the
material.
• Glass, rubber, wood are
good insulators.
– Natural fibers are usually
good insulators.
• Humans can be good
insulators.
Conduction vs Induction
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Conduction occurs between
objects in contact with each
other.
• The object being charged has
no way for the charge to
escape once it is being
charged.
• The object doing the charging
loses charge that is gained by
the other object.
– That way the newly charged
object is left with the same
charge of the other object.
• Induction occurs between two
objects not in contact with each
other.
• The object being charged does
have a path for charges to
escape.
– That is because the object is
grounded, or attached to the
unlimited supply of electrons in
the Earth.
• Induction lines opposite
charges up along the surface
of the objects.
– This pushes the electrons
toward the grounded surface
and the charge flows into the
Earth.
Polarization
• The shifting of the centers of charge to
favor one side of a molecule or the other is
called polarization.
• This often occurs in insulators.
• Also occurs in water because of the unique
molecule arrangement between oxygen
and hydrogen.
Coulomb’s Law
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Charles Coulomb (1736-1806) established the
fundamental laws that govern electric force
between two stationary charged sources
1. The electric force is inversely proportional to the
square of the separation, r, between the charges.
2. The electric force is proportional to the product of
the magnitudes of the charges, |q1| and |q2|
3. It is attractive if the charges are of opposite sign and
repulsive if the charges have the same sign.
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So you add the sign in after working the computations.
Coulomb the Electrical Newton?
• Coulomb’s Law is the electrical equivalent of Newton’s
Universal Law of Gravitation.
– Remember that stated there was an attractive force between all
objects depending on mass and separation.
• The set up is the same and must fit the laws stated by
Coulomb’s Law
F=
ke
Lowercase q stands for charge
|q1| |q2| Measured in Coulombs (C)
r2
r is the separation between charges
ke is the Coulomb Constant and is equal to 8.99 x 109 N•m2/C2
e- = -1.60 x 10-19 C
e+ = 1.60 x 10-19 C
e+ is called a proton
Superposition Principle
• When trying to find the electric force exerted on a charge
by other charges, you must add all the effect of all
charges vectorally.
• This process is called the superposition principle of
point charges.
– Find the individual forces using Coulomb’s Law
– Then add those two values just like we add vectors.
q3 +
q1
F21
Force on 2 by 1
Resultant Force
+
q2
Force on 2 by 3
F23
The Electric Field
E=
• Charged particles can have a varying effect on each
other in space.
– Touching or not touching!
• This effect was best described by Michael Faraday (1791-1867).
• An electric field exists in the region of space around a
charged object.
– When another charged object enters this region, an electrical
force becomes present between them.
• The direction of the field always points from positive to
negative.
• The strength of the field is defined as the magnitude of
the electric force divided by the magnitude of its charge.
– SI Units: N/C
q0 is the reference charge, or center of the charge pattern
F
q0
Electric Field From a
Single Point
• Another way to calculate the electric field generated by
single point charge is to ask for the help of Coulomb’s
Law
– Use this formula if the electric force is unknown.
E=
F=
q0
E = ke
q
r2
ke
|q| |q0|
r2
q0
Electric Field Lines
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Remember that the electric field points in a
direction from positive to negative.
An electric field line shows the path and
magnitude of the electric field present around a
single point charge.
1. Lines always point straight away from charge
2. The number of lines per unit area identify the field
strength
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The field is larger when the lines are closer together.
Drawing Field Lines
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Follow these rules for
drawing field lines
1.
Lines must begin at positive and
end at negative.
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2.
-
+
+
If there is no positive, start at
infinity.
If no negative, end at infinity.
The number of lines drawn is
proportional to the magnitude of
the charge.
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3.
+
More lines, larger the charge.
No two field lines cross each
other.
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They may connect, but they
never cross.
Electrostatic Equilibrium
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When no net motion of charge occurs within a
conductor, the conductor is said to be at
electrostatic equilibrium.
An isolated conductor (Insulated from ground) has the
following properties:
1. Electric field is zero inside the conductor.
2. All charge resides entirely on its surface.
3. Electric field just outside a charged conductor is
perpendicular to the surface.
4. On irregularly shaped conductors, the charge tends
to accumulate at locations of the smallest radius of
curvature, or tightest corners.
Electric Flux
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As an electric field passes through a given
area, the amount of charge carriers can vary
depending on the size of the area and the
strength of the field.
That rate is called electric flux.
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Electric flux is much like the flow rate of
charge carriers.
Important characteristics when
identifying electric flux
1. The field is the strongest when it is
perpendicular to the surface.
2. The field is zero when it is parallel to the surface.
Φ = EA cos θ
θ is the angle made between the “perpendicular” surface and the surface itself. (90 – α)
Enclosed Regions
• When the area is constructed as to create an enclosed
region
– The flux lines entering the interior are negative.
– The flux lines leaving the interior are positive.
Gauss’s Law
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That enclosed surface is often called a gaussian surface.
The flux transferred through a closed surface can be then described by
Gauss’s Law.
• Karl Friedrich Gauss (1777-1855)
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Gauss’s Law states the net electric flux through any closed gaussian
surface is equal to the net charge inside the surface divided by 0.
– 0 is called the permittivity of free space.
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0 = 8.85 x 10-12 C2/(Nm2)
– constant for all materials under all conditions
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Coulomb’s Constant uses the permittivity of free space constant as
given from a spherical surface.
– kc = 1/4
Σ Φ = Σ EA cos θ =
Q
0