Transcript test charge

Ch. 21
The Electric Field I:
Discrete Charge
Distributions
Ch. 21 Overview
 Properties
of Charge
 Conductors and Insulators
 Forces between Charges
 Comparison of the Electrostatic and
Gravitational Forces
 The Electric Field
 Electric Dipoles in Electric Fields
Which of the following are
fundamental properties of
matter?
(CT)
1.
2.
3.
4.
5.
1
Mass
Charge
Spin
1 and 2
1,2, and 3
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Charge
If you rub a piece of
amber with fur the
amber will attract bits
of paper
 Greek term for amber –
Elektronos from which
we derive electron
 If two amber rods are
brought together, they
will repel

If charges can attract or repel
each other then what do they
exert on each other?
(GR)
What does it suggest about
charges that the force between
them can be both attractive and
repulsive?
(GR)
How is this different than the
force between masses?
(Gravity)
(GR)
If a piece of fur is rubbed against an
amber rod, the amber rod becomes
negatively charged. What is the
sign of the charge of the fur? (TPS)
Negative
Positive
It is uncharged
Cannot be
determined
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If a piece of fur is rubbed against an
amber rod, the amber rod becomes
negatively charged. What is the sign of
the charge of the fur? (CT)
1.
2.
3.
4.
Negative
Positive
It is uncharged
Cannot be determined
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Properties of Charge
 Charges
exert forces on each other
 Forces can be repulsive or attractive
 Two Types of Charge called +/- due
to Franklin
 Like charges repel, opposite charges
attract
 Charge is conserved
 Charge is quantized
Quantization of Charge
Basic unit of charge is the charge of an
electron
 e = -1.602 x 10-19 C
 The charge of a proton is opposite the
charge of the electron
p = 1.602 x 10-19 C = |e|
 SI (derived) unit of charge is the coulomb,
C

Quantization of Charge (cont.)
 The
charge, q, on any object can be
expressed as q = Ne where N is
some integer
 Fundamental SI units 1 C = 1 As
(ampere second)
Ex: How many electrons are
there in -1 C of charge?
Solution:
q = Ne
Solve for N
N = q/e
N = -1 C/ -1.602 x 10-19 C
N = 6.2 x 1018 electrons
A student makes the following statement. When I rub a
piece of glass with silk, the glass obtains 17.5 charges
and silk has -11.3. What if anything is wrong with the
students statement? (TPS)
The statement contains no errors
1.
The statement violates charge
conservation
The statement violates charge
quantization
2 and 3
Cannot be determined
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3.
4.
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A student makes the following statement. When I rub a
piece of glass with silk, the glass obtains 17.5 charges
and silk has -11.3. What if anything is wrong with the
students statement? (TPS)
The statement contains no errors
The statement violates charge
conservation
The statement violates charge
quantization
2 and 3
Cannot be determined
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2.
3.
4.
5.
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Insulators and Conductors
What is the difference between an
insulator and a conductor? (BRST)
Insulators and Conductors
 In
an Insulator all of the electrons
are strongly localized around an
individual atom
 In a Conductor about one electron
per atom is shared by the metal as a
whole. This electron is called a free
electron
Two uncharged metal
spheres are in contact. A
negatively charge amber rod
is brought near one of the
spheres. Draw a sketch
showing the charge
distribution on the spheres.
+
+
-
The electroscope
Simple Device
Used to indicate
charge
 Two metal foil
leaves are
suspended from
the bottom of a
conducting rod

Electroscope Demonstration
 What
happens when a charged
insulating rod is brought near the
electroscope?
 What happens when a charge
insulating rod is rubbed against the
electroscope?
 What happens when you bring your
hand near the electroscope?
 What happens when you touch the
charged electroscope?
A piece of PVC pipe is rubbed with a piece of fur
and then brought near an empty aluminum can
lying on its side. What will happen to the can?
(TPS)
Nothing
It will be repelled
from the can
It will be attracted
to the can
It cannot be
determined
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2.
3.
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A piece of PVC pipe is rubbed with a piece of fur
and then brought near an empty aluminum can
lying on its side. What will happen to the can?
Nothing
It will be repelled
from the can
It will be attracted
to the can
It cannot be
determined
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2.
3.
4.
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Insulators vs. Conductors
An uncharged plastic rod is placed on the
bulb of an electroscope. A charged plastic
rod is brought near the other plastic rod
but away form the electroscope. What will
happen?
 A piece of metal is placed on the bulb of
an electroscope. A charge plastic rod is
brought near the other plastic rod but
away form the electroscope. What will
happen?

A plastic rod is charged and brought
near a few small pieces of paper. What
will happen to the paper?
Nothing since the paper is an
insulator
The paper will be attracted to
the rod
The paper will be repelled by
the rod
Cannot be determined
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How is it possible that the
insulating paper can be
attracted to the rod?
Induced Polarization



Bringing a charge near
an insulator can cause
a slight
rearrangement of the
electrons around the
nucleus of the atom
The insulator can then
be slightly attracted to
charge
Ex. Rub a balloon on
your head and stick it
to the wall
Coulomb’s Law
Like charges repel
 Opposite charges
attract
 Force depends
inversely on the
square of the
distance between
the charges

Charles Coulomb

Determined form
of force between
charges using a
torsional balance
Coulomb’s Law

q1q 2
F  k e 2 rˆ
r
q1
r
q2
Coulomb’s Law
 ke
 ε0
= 8.99 x 109 N m2/C2
= 8.85 x 10-12 C2/Nm2 (Ch. 19)
ke 
1
40
Two positive charges are separated by
a known distance. The distance is then
doubled, how does this affect the force?
(TPS)
1.
2.
3.
4.
5.
6.
1
2
The force is unchanged
The force is doubled
The force is halved
The force is quadrupled
The force is reduced by ¼
Cannot be determined
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Two positive charges are separated by a
known distance. The distance is then
doubled, how does this affect the force?
1.
2.
3.
4.
5.
6.
1
2
The force is unchanged
The force is doubled
The force is halved
The force is quadrupled
The force is reduced by ¼
Cannot be determined
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Ex. Find the magnitude and
direction of the force on charge
1 shown below.
q1 = 2.5 µC
.25 m
q2 = -3.0 μC
Solution
F = kq1q2/r2
= 8.99 x 109 Nm2/C2 x 2.5 x 10-6 C x 3.0 x 106C/(.25
m)2
= .27 N
The direction is down.
How will the force on charge 1
compare to the force on charge
2?
(CT)
1.
2.
3.
4.
It will be larger
It will be the same
It will be smaller
Cannot be determined
without first calculating the
answer
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A student measures the force on each of two
charged objects due to the other. She finds
the forces to be the same in magnitude and
opposite in direction. Which of the following
is true about the charges? (CT)
The charges must be identical
The charges are equal in magnitude and
of opposite sign
The charges must have the same sign
but can have different magnitudes
The charges must have opposite signs
but can have different magnitudes
Cannot be determined
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In what ways is Coulomb’s
Law similar to Newton’s Law
of Gravity?
What is a significant
difference Coulomb’s Law
and Newton’s Law of Gravity
Comparison of Newton’s Law of
Gravity and Coulomb’s Law

q1q 2
F  k e 2 rˆ
r

m1m2
F  G 2 rˆ
r
Inverse Square Law
Strength is
proportional to
product of “source”
terms
Gravity is always
attractive
Electrostatic Force
can be both
attractive and
repulsive
Ex. Find the ratio of the
electrostatic force between
two protons and the
gravitational force between
them if they are separated by
.25 m.
Solution
q1q2
2
Fe
r

mm
Fg
G 12 2
r
k e q1q2 r 2

r 2 Gm1m2
ke

k e q1q2
Gm1m2
m2
8.99 10 N 2 1.602 10 19 C 1.602 10 19 C
C

2
m
6.67 10 11 N 2 1.67 10  27 kg 1.67 10  27 kg
kg
9
= 1.24 x 1036
 The
electrostatic force is much
stronger
 Protons are like charges and thus in
a nucleus of an atom will repel each
other
 Gravity is not strong enough to hold
the nucleus together
 Nucleus is held together by short
range force called the “Strong Force”
The Electric Field
There’s a core question about
long range forces such as the
electrostatic force or the
gravitational force.
If two charges are separated by a
distance, then how do they
“know” there is a force between
them.
The Electric Field
Newton’s answer for
gravity was that they
just do – “Action at a
distance.”
 Michael Faraday
borrowed an idea from
magnetism and
introduced tubes of
force

Definition of the Electric Field
 Consider
a small positive charge
called a test charge, q0 brought near
a positive charge, Q
Q
q0
Which of the following is the correct force
vector on the test charge q0?
1.
2.
3.
4.
None of the above is correct
5.
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Suppose the test charge was
moved further away from the
charge Q, how will the force
vector change?
1.
2.
3.
4.
1
2
It will be larger
It will be smaller
It will not change
Cannot be
determined
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Suppose the test charge was
moved closer to the charge Q,
how will the force vector
change?
1.
2.
3.
4.
1
2
It will be larger
It will be smaller
It will not change
Cannot be
determined
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Definition of the Electric Field
 The
test charge will feel a force
anywhere it is placed
 The “source” charge affects the
space around it
 The effect on the space around it is
the electric field
 We test the electric field with the test
charge, but the electric field is due to
the source charge
Definition of the Electric Field


F
E  lim
q0  0 q
0
Definition of the Electric Field
 Electric
field is force per charge
 The electric field is defined so that
the test charge is positive
 Units – N/C
Ex. A force 0f .25 N is exerted
to the left on a test charge of
magnitude q0 = 2 μC. a)
Sketch the situation. b) What is
the magnitude and direction of
the electric field at the location
of the test charge?
Ex. A test charge of magnitude is
located in an electric field of
magnitude 200 N/C directed to the
right. a) Sketch the situation. b)
Find the magnitude and direction of
the force on the test charge.
The Electric Field due to a Point
Charge
 We
can use coulombs law to find the
electric field due to a point charge, Q
Q
r
q0
The Electric Field due to a Point
Charge

Force on the test charge (by definition
positive) is given by
Qq 0
F k 2
r
The Electric Field due to a Point
Charge
Electric field is
defined as
 E = F/q0
 So

Qq 0 1
Ek 2
r q0
Q
k 2
r
The Electric Field due to a Point
Charge
 This
result is also usually known as
Coulomb’s law
If the source charge Q is positive, what is
the direction of the electric field at the
location of the test charge? (CT)
To the right
To the left
Up
Down
Cannot be determined
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If instead the source charge Q is negative,
what is the direction of the electric field at
the location of the test charge? (CT)
To the right
To the left
Up
Down
Cannot be determined
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2.
3.
4.
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Ex. A point P is 3.0 cm north of
a charged point particle with
charge Q = 3.5 pC. a) Sketch
the situation. b) Find the
magnitude and direction of the
electric field at the point P.
Superposition
 The
electric field at a point due to
several charges is the sum of the
field due to the individual charges
 Since the electric field is a vector,
vector algebra must be used to find
the sum
FPE Exercise on Electric Fields
Electric Fields in Conductors in
Electrostatic equilibrium
A
piece of metal is placed in a
constant electric field. Sketch a
picture of what happens to the
charge in the metal
 When does the charge separation
stop?
Electric Fields in Conductors in
Electrostatic equilibrium
A
conductor in electrostatic
equilibrium has an electric field of 0
inside the conductor