Chapter 15 Electric Charge

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Chapter 15 Electric Charge
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Main Points of Chapter 15

• Charge
• Electric forces
• Two types of charge
• Induction
• Conservation and quantization of charge
• Coulombs law
• Forces involving multiple charges

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15-1 Chargea Property of Matter

• A Brief History of the Study of Electricity
• and Magnetism

2. The Significance of Electric Forces
The Electric Force is responsible for

• electrons binding to a positive nucleus,
• forming a stable atom

• atoms binding together into molecules

• atoms or molecules binding together into
• liquids and solids

• forces such as friction and other contact forces

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3. Matter and Electric Charge
1) The Origin of Charge
The atom is electrically neutral
number of e number of p
Charge is an intrinsic property of matter
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2) Conductors and Insulators
Materials in which the outermost electron(s) that
are very loosely bound to the atoms, and can move
freely through the material are called
conductors.

• metal

Materials in which charge does not move easily
are called insulators.

• glass, plastics, paper

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A Electrons are free to move in a conductor.
A Electrons stay with their atom in an insulator.
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3) Charging by friction
We can transfer charge from one material to
another suitable material simply by rubbing
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Electric charges are of two types, called
positive () and negative (-)
Like charges repel, and unlike charges attract.
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We know that when glass is rubbed with silk,
electrons are transferred from the glass to the
silk. Because the silk is negatively charged,
electrons are said to carry a negative charge
Electrons have a negative charge because of a
historical choice rather than because of an
intrinsic physical property.
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In the presence of a charged object, a neutral
object can polarize the charges opposite to
those on the charged object move closer to it,
and the other charges move away.
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4) Charging by Induction
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Charge is measured in Coulombs (C)
The smallest unit of charge is the magnitude of
the charge on the electron
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• ACT Two neutral conductors are connected by a
  wire and a charged rod is brought near, but does
  not touch. The wire is taken away, and then the
  charged rod is removed. What are the charges on
  the conductors?

Follow-up What will happen when the conductors
are reconnected with a wire?
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4. The Electroscope
The electroscope is a device that detects the
presence of excess free charge on an object. This
can be done in two ways
First, when a charged rod transfers charge
directly to the electroscope, that charge spreads
uniformly over its metal surfaces. The leaf and
stem then have same-sign charges, and repel.
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Second, when a charged rod is brought near, but
not touching, the electroscope, it attracts
opposite charges. The like charges tend to move
away from the rod once again the stem and leaf
have same-sign charges, and repel.
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15-2 Charge is Conserved and Quantized
1.Charge is conserved
Charge by friction
Charge by Induction
In observed reactions involving the so-called
elementary particles, no one has ever seen a
single case of net charge appearing or
disappearing.
Radioactive decay of nuclei
The algebraic sum of all the electric charges in
any closed system is constant.
Principle of conservation of charge
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2.Charge is quantized
Free charge is quantized in positive or negative
integral multiples of e
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15-3 Coulombs Law
1. Point charge (charged particle)
a point-like object with none zero electric charge
Coulombs torsion balance
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2. Coulombs law

• The electric force between charges q1 and q2 is
• attractive if charges have opposite signs
• repulsive if charges have same signs

The magnitude F of the electric force between two
point charges is directly proportional to the
product of the charges and inversely proportional
to the square of the distance between them.
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Where k is a proportionality constant whose
numerical value depends on the units used for
charge.
the permittivity of free space
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3. Define the Columb
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• Act How many electrons are there in one coulomb
• of negative charge?

Solution
The number of electrons is equal to the charge q
divided by the charge e on each electron.
The number N of electrons is
This number is enormous.
There is as much as 25 coulombs can be
transferred between the cloud and the ground in
a lightning bolt. The typical charges produced
in the laboratory are much smaller and are
measured conveniently in microcoulombs.
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4. Discussion

• Coulombs law describes only the interaction
• of two point charges

b. The two forces obey Newtons third law
c. Electric force vs. gravitational force.
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• Example The nucleus in an iron atom has a radius
  of about 4.0   10-15 m and contains 26 protons.
• (a)  What is the magnitude of the repulsive
  electrostatic force between two of the protons
  that are separated by 4.0   10-15 m?

(b)  What is the magnitude of the gravitational
force between those same two protons?
Solution
The gravitational force is negligible in
comparison to the electrostatic force.
The protons are bound together by an enormous
force called the strong nuclear force.
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15-4 Forces Involving Multiple Charges
1. Principle of Superposition
When there are multiple charges, the net
force on any one of them is the vector sum of the
forces due to each of the others.
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• ACT A circular ring of charge of radius a and
  total charge Q lies in the x-y plane with it
  center at the origin. The direction of the force
  on a very small segment of this ring is directed
  ________ if Q is negative.
• A) along the negative z-axis
• B) in no direction since the force is zero
• C) outward from the origin
• D) inward toward the origin
• E) along the positive z-axis

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• ACT Three equal charges are located at the
  corners of an equilateral triangle. If the length
  of the sides of the triangle are doubled and each
  of the charges is doubled, then the resulting
  force on each of the charges ________
• A) doubles.
• B) quadruples.
• C) is halved.
• D) stays the same.
• E) changes by a factor of 1.414.

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2. Continuous Distributions of Charges
For a continuous distribution of charge, first
think of it as a collection of very small charges
The total force is found by summing the force
from each piece
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If we know the charge density as a function of
position, we can go to the limit where the
charges are infinitesimally small, and integrate.
Q
l the linear charge density
s the surface charge density
r the volume charge density
In practice, such integrals involve three
one-dimensional integrals.
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• Example Figure below shows two particles fixed
  in place a particle of charge q1 8q at the
  origin and a particle of charge q2 -2q at x
  L. At what point (other than infinitely far away)
  can a proton be placed so that it is in
  equilibrium (meaning that the net force on it is
  zero)? Is that equilibrium stable or unstable?

Solution
If the proton at point R
The equilibrium at x2L is unstable
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• Example A point charge Q is located at a
  distance a from one end of a charged object with
  electric line density ? and length L, as shown in
  the following figure. Find the force on the
  charge Q.

Solution
Q
a
O
x
L
left
If Lltlt a , F ?
point charge result
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• Example A charge is spread uniformly along the
• y-axis from y0 to The charge
  density on
• the y-axis is l Find the force on a point
  charge q
• placed on the x-axis at xx0

y
Solution
q
x
x0
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• Example Find the force on a point charge q1
  located
• on the axis of a uniformly charged ring of total
  charge q
• The radius of the ring is R, and q1 is located a
  distance x
• from the center of the ring.

Solution
R
q1
x
x
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If x0,
If xgtgtR
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• Example Calculate the force exerted on a charge
  q1 by
• an infinite plane sheet with surface charge
  density
• (charge per unit area) s.

s
Solution
q1
Break up the plane into concentric rings.
x
x
Use the results of last example
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3. The Force Due to a Spherical Symmetric
Charge Distribution
The two shell theorems
A shell of uniform charge attracts or repels a
charged particle that is outside the shell as if
all the shell's charge were concentrated at its
center.
If a charged particle is located inside a shell
of uniform charge, there is no net electrostatic
force on the particle from the shell.
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If a charge distribution is spherically symmetric
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Summary of Chapter 15

• Electric charge comes in two types, positive and
  negative.
• Opposite charges attract like charges repel.
• Metals are good conductors electrons are able
  to move freely through them most other materials
  are insulators
• Basic charge is that on the electron

• All other charges are multiples of e.

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Summary of Chapter 15, cont.

• Charge is conserved net charge before an
  interaction is the same as net charge afterwards
• Coulombs law for the force between two point
  charges

• For multiple, or continuous, charges, the
  superposition principle applies.