Electric Charge and Electric Field

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Electric Charge and Electric Field
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• Static Electricity Electric Charge and Its
  Conservation
• Electric Charge in the Atom
• Insulators and Conductors
• Induced Charge the Electroscope
• Coulombs Law
• The Electric Field
• Electric Field Calculations for Continuous
  Charge Distributions

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• Field Lines
• Electric Fields and Conductors
• Motion of a Charged Particle in an Electric
  Field
• Electric Dipoles
• Electric Forces in Molecular Biology DNA
• Photocopy Machines and Computer Printers Use
  Electrostatics

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Electric Charge and Its Conservation
Charge comes in two types, positive and negative
like charges repel and opposite charges attract.
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Electric Charge and Its Conservation
Electric charge is conserved the arithmetic sum
of the total charge cannot change in any
interaction.
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Electric Charge in the Atom
Atom Nucleus (small, massive, positive
charge) Electron cloud (large, very low density,
negative charge)
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Insulators and Conductors
Conductor Charge flows freely Metals
Insulator Almost no charge flows Most other
materials
Some materials are semiconductors.
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Coulombs 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.
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Coulombs Law
Coulombs law
This equation gives the magnitude of the force
between two charges.
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Coulombs Law
Unit of charge coulomb, C. The proportionality
constant in Coulombs law is then k 8.99 x 109
Nm2/C2.
Charges produced by rubbing are typically around
a microcoulomb 1 µC 10-6 C.
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Coulombs Law
Charge on the electron e 1.602 x 10-19 C.
Electric charge is quantized in units of the
electron charge.
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Coulombs Law
The proportionality constant k can also be
written in terms of e0, the permittivity of free
space
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Coulombs 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.
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Coulombs Law
In its vector form, the Coulomb force is
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Coulombs Law
Three charges in a line. Three charged particles
are arranged in a line, as shown. Calculate the
net electrostatic force on particle 3 (the -4.0
µC on the right) due to the other two charges.
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Coulombs Law
Electric force using vector components. Calculate
the net electrostatic force on charge Q3 shown in
the figure due to the charges Q1 and Q2.
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The Electric Field
The electric field is defined as the force on a
small charge, divided by the magnitude of the
charge
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The Electric Field
An electric field surrounds every charge.
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The Electric Field
For a point charge
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The Electric Field
Force on a point charge in an electric field
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The Electric Field
Electric field of a single point
charge. Calculate the magnitude and direction of
the electric field at a point P which is 30 cm to
the right of a point charge Q -3.0 x 10-6 C.
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The Electric Field
E at a point between two charges. Two point
charges are separated by a distance of 10.0 cm.
One has a charge of -25 µC and the other 50 µC.
(a) Determine the direction and magnitude of the
electric field at a point P between the two
charges that is 2.0 cm from the negative charge.
(b) If an electron (mass 9.11 x 10-31 kg) is
placed at rest at P and then released, what will
be its initial acceleration (direction and
magnitude)?
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The Electric Field
E above two point charges. Calculate the total
electric field (a) at point A and (b) at point B
in the figure due to both charges, Q1 and Q2.
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The Electric Field

• Problem solving in electrostatics electric
  forces and electric fields
• Draw a diagram show all charges, with signs,
  and electric fields and forces with directions.
• Calculate forces using Coulombs law.
• Add forces vectorially to get result.
• Check your answer!

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Continuous Charge Distributions
A continuous distribution of charge may be
treated as a succession of infinitesimal (point)
charges. The total field is then the integral of
the infinitesimal fields due to each bit of
charge
Remember that the electric field is a vector you
will need a separate integral for each component.
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Continuous Charge Distributions
A ring of charge. A thin, ring-shaped object of
radius a holds a total charge Q distributed
uniformly around it. Determine the electric field
at a point P on its axis, a distance x from the
center. Let ? be the charge per unit length (C/m).
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Continuous Charge Distributions
Charge at the center of a ring. Imagine a small
positive charge placed at the center of a
nonconducting ring carrying a uniformly
distributed negative charge. Is the positive
charge in equilibrium if it is displaced slightly
from the center along the axis of the ring, and
if so is it stable? What if the small charge is
negative? Neglect gravity, as it is much smaller
than the electrostatic forces.
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Continuous Charge Distributions
Long line of charge. Determine the magnitude of
the electric field at any point P a distance x
from a very long line (a wire, say) of uniformly
distributed charge. Assume x is much smaller than
the length of the wire, and let ? be the charge
per unit length (C/m).
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Continuous Charge Distributions
Uniformly charged disk. Charge is distributed
uniformly over a thin circular disk of radius R.
The charge per unit area (C/m2) is s. Calculate
the electric field at a point P on the axis of
the disk, a distance z above its center.
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Continuous Charge Distributions
In the previous example, if we are very close to
the disk (that is, if z ltlt R), the electric field
is
Infinite plane
This is the field due to an infinite plane of
charge.
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Continuous Charge Distributions
Two parallel plates. Determine the electric field
between two large parallel plates or sheets,
which are very thin and are separated by a
distance d which is small compared to their
height and width. One plate carries a uniform
surface charge density s and the other carries a
uniform surface charge density -s as shown (the
plates extend upward and downward beyond the part
shown).
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Field Lines
The electric field can be represented by field
lines. These lines start on a positive charge and
end on a negative charge.
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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.
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Field Lines
Electric dipole two equal charges, opposite in
sign
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Field Lines
The electric field between two closely spaced,
oppositely charged parallel plates is constant.
uniform field
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Field Lines

• Summary of field lines
• Field lines indicate the direction of the field
  the field is tangent to the line.
• The magnitude of the field is proportional to the
  density of the lines.
• Field lines start on positive charges and end on
  negative charges the number is proportional to
  the magnitude of the charge.

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Conductors
The static electric field inside a conductor is
zero if it were not, the charges would
move. The net charge on a conductor resides
on its outer surface.
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Conductors
The electric field is perpendicular to the
surface of a conductor again, if it were not,
charges would move.
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Conductors
Shielding, and safety in a storm. A neutral
hollow metal box is placed between two parallel
charged plates as shown. What is the field like
inside the box?
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Motion in an Electric Field
The force on an object of charge q in an electric
field is given by
q Therefore, if we know the mass and
charge of a particle, we can describe its
subsequent motion in an electric field.
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Motion in an Electric Field
Electron accelerated by electric field. An
electron (mass m 9.11 x 10-31 kg) is
accelerated in the uniform field (E 2.0 x
104 N/C) between two parallel charged plates. The
separation of the plates is 1.5 cm. The electron
is accelerated from rest near the negative plate
and passes through a tiny hole in the positive
plate. (a) With what speed does it leave the
hole? (b) Show that the gravitational force can
be ignored. Assume the hole is so small that it
does not affect the uniform field between the
plates.
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Motion in an Electric Field
Electron moving perpendicular to . Suppose an
electron traveling with speed v0 1.0 x 107 m/s
enters a uniform electric field , which is at
right angles to v0 as shown. Describe its motion
by giving the equation of its path while in the
electric field. Ignore gravity.
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Electric Dipoles
An electric dipole consists of two charges Q,
equal in magnitude and opposite in sign,
separated by a distance . The dipole moment, p
Q , points from the negative to the positive
charge.
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Electric Dipoles
An electric dipole in a uniform electric field
will experience no net force, but it will, in
general, experience a torque
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Electric Dipoles
The electric field created by a dipole is the sum
of the fields created by the two charges far
from the dipole, the field shows a 1/r3
dependence
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Electric Dipoles
Dipole in a field. The dipole moment of a water
molecule is 6.1 x 10-30 Cm. A water molecule is
placed in a uniform electric field with magnitude
2.0 x 105 N/C. (a) What is the magnitude of the
maximum torque that the field can exert on the
molecule? (b) What is the potential energy when
the torque is at its maximum? (c) In what
position will the potential energy take on its
greatest value? Why is this different than the
position where the torque is maximum?
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Summary

• Two kinds of electric charge positive and
  negative.
• Charge is conserved.
• Charge on electron
• e 1.602 x 10-19 C.
• Conductors electrons free to move.
• Insulators nonconductors.

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Summary

• Charge is quantized in units of e.
• Objects can be charged by conduction or
  induction.
• Coulombs law
• Electric field is force per unit charge

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Summary

• 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.

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Gausss Law
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• Electric Flux
• Gausss Law
• Applications of Gausss Law
• Experimental Basis of Gausss and Coulombs Laws

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Electric Flux
Electric flux
Electric flux through an area is proportional to
the total number of field lines crossing the area.
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Electric Flux
Electric flux. Calculate the electric flux
through the rectangle shown. The rectangle is 10
cm by 20 cm, the electric field is uniform at 200
N/C, and the angle ? is 30.
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Electric Flux
Flux through a closed surface
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Gausss Law
The net number of field lines through the surface
is proportional to the charge enclosed, and also
to the flux, giving Gausss law
This can be used to find the electric field in
situations with a high degree of symmetry.
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Gausss Law
For a point charge,
Therefore,
Solving for E gives the result we expect from
Coulombs law
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Gausss Law
Using Coulombs law to evaluate the integral of
the field of a point charge over the surface of a
sphere surrounding the charge gives
Looking at the arbitrarily shaped surface A2, we
see that the same flux passes through it as
passes through A1. Therefore, this result should
be valid for any closed surface.
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Gausss Law
Finally, if a gaussian surface encloses several
point charges, the superposition principle shows
that
Therefore, Gausss law is valid for any charge
distribution. Note, however, that it only refers
to the field due to charges within the gaussian
surface charges outside the surface will also
create fields.
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Applications of Gausss Law
Spherical conductor. A thin spherical shell of
radius r0 possesses a total net charge Q that is
uniformly distributed on it. Determine the
electric field at points (a) outside the shell,
and (b) within the shell. (c) What if the
conductor were a solid sphere?
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Applications of Gausss Law
Solid sphere of charge. An electric charge Q is
distributed uniformly throughout a nonconducting
sphere of radius r0. Determine the electric field
(a) outside the sphere (r gt r0) and (b) inside
the sphere (r lt r0).
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Applications of Gausss Law
Nonuniformly charged solid sphere. Suppose the
charge density of a solid sphere is given by ?E
ar2, where a is a constant. (a) Find a in terms
of the total charge Q on the sphere and its
radius r0. (b) Find the electric field as a
function of r inside the sphere.
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Applications of Gausss Law
Long uniform line of charge. A very long straight
wire possesses a uniform positive charge per unit
length, ?. Calculate the electric field at points
near (but outside) the wire, far from the ends.
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Applications of Gausss Law
Infinite plane of charge. Charge is distributed
uniformly, with a surface charge density s (s
charge per unit area dQ/dA) over a very large
but very thin nonconducting flat plane surface.
Determine the electric field at points near the
plane.
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Applications of Gausss Law
Electric field near any conducting
surface. Show that the electric field just
outside the surface of any good conductor of
arbitrary shape is given by E
s/e0 where s is the surface charge density on
the conductors surface at that point.
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Applications of Gausss Law

• The difference between the electric field outside
  a conducting plane of charge and outside a
  nonconducting plane of charge can be thought of
  in two ways
• The field inside the conductor is zero, so the
  flux is all through one end of the cylinder.
• The nonconducting plane has a total charge
  density s, whereas the conducting plane has a
  charge density s on each side, effectively giving
  it twice the charge density.

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Applications of Gausss Law
Conductor with charge inside a cavity. Suppose a
conductor carries a net charge Q and contains
a cavity, inside of which resides a point
charge q. What can you say about the charges
on the inner and outer surfaces of the
conductor?
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Applications of Gausss Law

• Procedure for Gausss law problems
• Identify the symmetry, and choose a gaussian
  surface that takes advantage of it (with surfaces
  along surfaces of constant field).
• Draw the surface.
• Use the symmetry to find the direction of E.
• Evaluate the flux by integrating.
• Calculate the enclosed charge.
• Solve for the field.

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Summary

• Electric flux
• Gausss law
• Gausss law can be used to calculate the field
  in situations with a high degree of symmetry.
• Gausss law applies in all situations, and
  therefore is more general than Coulombs law.