Transcript 16.7 The Electric Field For a point charge

Lecture PowerPoints
Chapter 16
Physics: Principles with
Applications, 6th edition
Giancoli
© 2005 Pearson Prentice Hall
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Chapter 16
Electric Charge and
Electric Field
Units of Chapter 16
• Static Electricity; Electric Charge and Its
Conservation
• Electric Charge in the Atom
• Insulators and Conductors
• Induced Charge; the Electroscope
• Coulomb’s Law
• Solving Problems Involving Coulomb’s Law and
Vectors
• The Electric Field
Units of Chapter 16
• Field Lines
• Electric Fields and Conductors
• Gauss’s Law
• Electric Forces in Molecular Biology: DNA
Structure and Replication
• Photocopy Machines and Computer
Printers Use Electrostatics
16.1 Static Electricity; Electric Charge
and Its Conservation
Objects can be charged by rubbing
16.1 Static Electricity;
Electric Charge and Its
Conservation
Charge comes in two
types, positive and
negative; like charges
repel and opposite
charges attract
16.1 Static Electricity; Electric Charge
and Its Conservation
Electric charge is conserved – the
arithmetic sum of the total charge cannot
change in any interaction.
16.2 Electric Charge in the Atom
Atom:
Nucleus (small,
massive, positive
charge)
Electron cloud (large,
very low density,
negative charge)
16.2 Electric Charge in the Atom
Atom is electrically neutral.
Rubbing charges objects by moving electrons
from one to the other.
16.2 Electric Charge in the Atom
Polar molecule: neutral overall, but charge not
evenly distributed
16.3 Insulators and Conductors
Conductor:
Insulator:
Charge flows freely
Almost no charge flows
Metals
Most other materials
Some materials are semiconductors.
16.4 Induced Charge; the Electroscope
Metal objects can be charged by conduction:
Charging by conduction means that contact
was made in the process.
Free electrons from the neutral object can pass
over to the positively charged object.
The two objects end up with the same net charge.
Induction does not allow the neutral object to be
touched by the charged object.
The free electrons do not leave the neutral object,
but instead move toward the positive charge.
Creates a charge at either ends of the metal rods,
so that if the rod was divided in half each half
would have a charge.
No net charge has been created, just a separation.
16.4 Induced Charge; the Electroscope
They can also be charged by induction:
-by use of a ground connecting
it to the Earth.
When the charge is brought
close, the electrons are repelled
and will leave through the
ground wire. Then if the ground
wire is cut the rod is left positively charged.
However, if the negatively charged rod is
removed before the ground wire is cut;
then the electrons will move back to the
rod.
16.4 Induced Charge; the Electroscope
Nonconductors won’t become charged by
conduction or induction, but will experience
charge separation:
16.4 Induced Charge; the Electroscope
The electroscope
can be used for
detecting charge:
The greater the amount
of charge, the greater the
leaves separate.
16.4 Induced Charge; the Electroscope
The electroscope can be charged either by
conduction or by induction.
Electroscopes can be used to determine the sign
of a charge, if it is first charged by conduction
with a negative charge.
Then if a negatively charged object is brought
close (induction) more electrons move down the
to the leaves and they move further apart.
And if a positively charged object is brought
close (induction) more electrons move away from
the leaves and the leaves come closer together.
16.4 Induced Charge; the Electroscope
The charged electroscope can then be used to
determine the sign of an unknown charge.
16.5 Coulomb’s Law
Experiment shows that the electric force
between two charges is proportional to the
product of the charges and inversely
proportional to the distance between them.
-double the charge on one object, then
the force doubles
-increase the distance, and the force
decreases with the square of the
distance.
16.5 Coulomb’s Law
Coulomb’s law:
(16-1)
This equation gives the magnitude of
the electric force that one object exerts
on a second.
The Gravitational Constant G can be determined by experiment. Its value was first
found by Henry Cavendish in 1798 with a device called a Cavendish balance. Two
identical masses are suspended from an extremely thin and delicate quartz fiber.
The two large masses can be moved close to the smaller masses and the attraction
between M and m will cause the fiber to twist. After calibrating the system so the
amount of force needed to produce a given twist is known and the attraction
force between m and M can be calculated and then solve for G.
F = G m1m2
r2
16.5 Coulomb’s Law
The force is along the line connecting the
charges, and is attractive if the charges are
opposite, and repulsive if they are the same.
Newton’s 3rd Law
16.5 Coulomb’s Law
Unit of charge: coulomb, C
The proportionality constant in Coulomb’s
law is then:
(9.0 X 10^9)
Charges produced by rubbing are
typically around a microcoulomb:
16.5 Coulomb’s Law
Charge on the electron:
Electric charge is quantized in units of the
electron charge.
charge on an electron –e / charge on a proton +e
Cannot lose a fraction of an electron, so the net
charge on any object must be a integral multiple
16.5 Coulomb’s Law
The proportionality constant k can also be
written in terms of
, the permittivity of free
space:
(16-2)
applies to objects whose size is much smaller than the
distance between them
16.5 Coulomb’s Law
Coulomb’s law strictly applies only to point charges.
-applies to charges when they are at rest which is known
as Electrostatics.
Superposition: for multiple point charges, the forces on each
charge from every other charge can be calculated and then added
as vectors.
16.6 Solving Problems Involving
Coulomb’s Law and Vectors
The net force on a charge is the vector
sum of all the forces acting on it.
16.6 Solving Problems Involving
Coulomb’s Law and Vectors
Vector addition review:
1. Calculate the magnitude of the force between
two 3.6 microcoulombs point charges 9.3 cm apart.
F= K Q1Q2
r
2
= (9 x 109)(3.6 x 10-6)2
=13.5 N
(.093)2
2. Find the force on the center charge.
+
Q1 = 4 uC
2m
Q2= -5 uC
4m
+
Q3= 6 uC
Calculate:F21= force on charge 2 by charge 1
F23= force on charge 2 by charge 3
3. Find the force on the +10uC charge in the figure below.
+
6 uC
30 cm
10 uC
+
20 cm
_
-8 uC
16.7 The Electric Field
The electric field is the
force charge, divided by
the charge:
(16-3)
16.7 The Electric Field
For a point charge:
(16-4a)
(16-4b)
16.7 The Electric Field
Force on a point charge in an electric field:
(16-5)
Superposition principle for electric fields:
16.7 The Electric Field
Problem solving in electrostatics: electric
forces and electric fields
1. Draw a diagram; show all charges, with
signs, and electric fields and forces with
directions
2. Calculate forces using Coulomb’s law
3. Add forces vectorially to get result
16.8 Field Lines
The electric field can be represented by field
lines. These lines start on a positive charge
and end on a negative charge.
The direction of the electric field is defined as the direction of
the electric force on a tiny, positive test charge, A test charge
is a fictitious charge endowed with a special quality: the test
charge exerts no forces on nearby charges and therefore
does not disturb the charges in the vicinity.
Electric Lines of Force:
-lines of force originate on and come out of positive
charges whereas, they are directed toward and end
on negative charges.
16.8 Field Lines
The number of field lines starting (ending)
on a positive (negative) charge is
proportional to the magnitude of the charge.
The electric field is stronger where the field
lines are closer together.
Which charge below has the greater magnitude?
How can you tell?
(b)
16.8 Field Lines
Electric dipole: two equal charges, opposite in
sign:
- field lines are curved and directed from the positive to the negative
-the direction of the electric field at any point is tangent to the field line at that point
What would happen to the field lines if the charges were equal and the same charge?
16.8 Field Lines
The electric field between
two closely spaced,
oppositely charged parallel
plates is constant.
The fringing of the plate near the edges can often be
ignored, especially if the separation of the plates is small
16.8 Field Lines
Summary of field lines:
1. Field lines indicate the direction of the
field; the field is tangent to the line.
2. The magnitude of the field is proportional
to the density of the lines.
3. Field lines start on positive charges and
end on negative charges; the number is
proportional to the magnitude of the
charge.
16.9 Electric Fields and Conductors
The static electric field inside a conductor is
zero – if it were not, the charges would move.
The net charge on a conductor is on its
surface.
16.9 Electric Fields and Conductors
The electric field is
perpendicular to the
surface of a conductor –
again, if it were not,
charges would move.
Electric field II to the surface would exert a force
on free electrons causing them to move
In static condition, the Ell must be zero.
Inside a nonconductor, which does not have free
electrons, a static field can exist.
If a metal box between two parallel charged plates is hollow
then the external field on the box is not changed since
the electrons are free to move to the surface. The inside of the
box is zero.
This is effective for shielding something delicate on the
inside of the box.
+
-
That is why it is safe inside a car during a lightning storm.
For a view of lightning hitting a cage containing a person:
http://www.youtube.com/watch?v=PT_MJotkMd8
16.10 Gauss’s Law
Relates electric charge and electric field
Involves Electric Flux which refers to the electric
field passing thru an area
Electric flux:
(16-7)
Electric flux through an
area is proportional to
the total number of field
lines crossing the area.
N∞ EAl
16.10 Gauss’s Law
Flux through a closed surface:
16.10 Gauss’s Law
The net number of field lines through the
surface is proportional to the charge
enclosed, and also to the flux, giving
Gauss’s law:
(16-9)
This can be used to find the electric field
in situations with a high degree of
symmetry.
16.11 Electric Forces in Molecular
Biology: DNA Structure and Replication
Molecular biology is the
study of the structure and
functioning of the living cell
at the molecular level.
The DNA molecule is a
double helix:
16.11 Electric Forces in Molecular
Biology: DNA Structure and Replication
The A-T and G-C
nucleotide bases
attract each other
through
electrostatic
forces.
16.11 Electric Forces in Molecular
Biology: DNA Structure and Replication
Replication: DNA is in a “soup” of A, C, G, and T in
the cell. During random collisions, A and T will be
attracted to each other, as will G and C; other
combinations will not.
16.12 Photocopy Machines and
Computer Printers Use Electrostatics
Photocopy machine:
• drum is charged positively
• image is focused on drum
• only black areas stay charged and
therefore attract toner particles
• image is transferred to paper and sealed by
heat
16.12 Photocopy Machines and
Computer Printers Use Electrostatics
16.12 Photocopy Machines and
Computer Printers Use Electrostatics
Laser printer is similar, except a computer
controls the laser intensity to form the image
on the drum
Summary of Chapter 16
• Two kinds of electric charge – positive and
negative
• Charge is conserved
• Charge on electron:
• Conductors: electrons free to move
• Insulators: nonconductors
Summary of Chapter 16
• Charge is quantized in units of e
• Objects can be charged by conduction or
induction
• Coulomb’s law:
• Electric field is force per unit charge:
Summary of Chapter 16
• Electric field of a point charge:
• Electric field can be represented by electric
field lines
• Static electric field inside conductor is zero;
surface field is perpendicular to surface
• Electric flux:
• Gauss’s law: