Chapter 16 Electric Field

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Chapter 16 Electric Field
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Main Points of Chapter 16

• Electric field
• Superposition
• Electric dipole
• Electric field lines
• Field of a continuous distribution of charge
• Motion of a charge in a field
• Electric dipole in external electric field

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16-1 Electric Field
1. Electric Field
Earlyan action-at-a-distance force
Later Faraday introduced Electric Field
E field
charge
Charge
Electric field
4
2. Definition of Electric field
Field Point
Size is small enough
Test charge
Charge is very small
source charge
Test charge must be small enough that it does not
affect field
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The electric field is defined
Some values of Electric fields
atmosphere at earths surface in clear weather
100-200 N/C
value sufficient to cause electrical breakdown
in dry air
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For a point charge
Therefore, the electric field of a point charge
is
The field points outwards from a positive charge
and inwards to a negative one
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Comparison of Electric Force with Electric Field

• Electric Force (F) - the actual force felt by a
  charge at some location.
• Electric Field (E) - found for a location only
  tells what the electric force would be if a
  charge were located there

A useful concept
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3. Principle of Superposition of Electric Fields
Since electric forces add by superposition, the
electric field does as well.
For a group of point charges
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• Act What is the electric field at the origin due
  to
• this set of charges?

a
a
Solution
q
q
a
a
Notice that the fields from the top-right and
bottom left cancel at the origin
a
q
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4. Electric Dipoles and Their Fields
An electric dipole is defined as equal and
opposite charges a distance l apart
electric dipole moment is defined as
and points from the negative charge towards the
positive one.
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Electric dipoles are often found in nature.
Charged objects can induce electric dipoles
(left) molecules may have permanent electric
dipole moments due to their structure (right).
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• Example Find the electric field of the electric
  dipole
• at point a and point b.

b
Solution
r
a
O
x
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Similarly, for point b,
b
r
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• ACT The electric field of a dipole at distance
  large compared to the charge separation ________
• A) decreases linearly with increasing distance.
• B) remains constant as the distance increases.
• C) decreases inversely with the cube of the
  distance.
• D) decreases inversely with the square of the
  distance.
• E) cannot be determined.

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16-2 Electric Field Lines
Electric field lines are a useful aid to
visualizing the electric field. There are two
rules to drawing these lines

• The electric field is tangent to the field line
  at every point.
• 2. The density of electric field lines is an
  indicator of relative field strength.

The next slide shows field lines for a point
charge, including the decrease in density as one
moves farther from the charge.
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Field lines of a positive point charge
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Left two equal, same-sign charges Right an
electric dipole
Important note We always draw only a few sample
field lines otherwise the sketch would be solid
color.
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Field Lines of two equal, same-sign charges

• There is a zero halfway between the two charges

• r gtgt a looks like the field of point charge
  (2q)

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Electric field lines have certain properties
which should be carefully noted

• Lines leave () charges and return to (-)
  charges,
• never discontinue in empty space
• Tangent of line direction of E
• Local density of field lines µ local magnitude
  of E

• No two field lines ever cross, even when
  multiple charges are present.

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• ACT What are the signs of the charges whose
  electric fields are shown at right?

Electric field lines originate on positive
charges and terminate on negative charges.
Which of the charges has the greater magnitude?
The red one
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16-3 The Field of a Continuous Distribution
To find the field of a continuous distribution of
charge, treat it as a collection of near-point
charges
Summing over the infinitesimal fields
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Finally, making the charges infinitesimally small
and integrating rather than summing
? linear charge density
? surface charge density
? volume charge density
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• Example An infinitely long wire is uniformly
  charged.
• The charge density is l .Find the Electric
  field at point
• P on the x-axis at xx0

y
Solution
P
x
x0
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The Electric Field produced by an infinite line
of charge is
- everywhere perpendicular to the line - is
proportional to the charge density
next lecture Gauss Law makes this trivial!!
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• ACT A long line of charge with charge per unit
  length ?1 is located on the x-axis and another
  long line of charge with charge per unit length
  ?2 is located on the y-axis with their centers
  crossing at the origin. In what direction is the
  electric field at point z a on the positive
  z-axis if ?1 and ?2 are positive?
• A) the positive z-direction
• B) halfway between the x-direction and the
  y-direction
• C) the negative z-direction
• D) all directions are possible parallel to the
  x-y plane
• E) cannot be determined

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• Act The figure here shows three nonconducting
  rods, one circular and two straight. Each has a
  uniform charge of magnitude Q along its top half
  and another along its bottom half. For each rod,
  what is the direction of the net electric field
  at point P?

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• Example A uniformly charged circular arc has
• radius R and subtends an angle 2q0.The total
  charge
• is q. Calculate the electric field at point P .

y
Solution
P
x
R
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• Act Find the electric field at point P on the
  axis
• of a uniformly charged ring of total charge q.
  The radius of the ring is R, the distance from P
  to the center of the ring is x.

Solution
P
R

• when x 0(P is at the center of the ring)

• when xgtgtR

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• Act Find the electric field at a distance x
  along the axis of a uniformly charged circular
  disk of radius R and charge Q

Solution
P
r
R
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P
If xgtgtR
r
R
Field of a point charge
If Rgtgtx
Field of an infinite uniformly charged plane
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Field of an infinite uniformly charged plane
Divide the plane into narrow straight strips
s
q1
x
x
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From the electric field due to a uniform sheet of
charge, we can calculate what would happen if we
put two oppositely-charged sheets next to each
other
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Summary of Electric Field Lines
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• Act A large flat has a uniform charge density s
  . A small
• circular hole of radius R has been cut in the
  middle of the
• surface. Calculate the electric field at point
  P(x)

Solution
Think that the configuration is composed of one
uniformly charged plane with charge density s
and a uniformly charged circular disk -s
R
. P
x
Use superposition
x
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• Example Find the electric field at point P on
  the central axis of the solid cone. The total
  charge is q

Solution
z
P
H
R
y
O
x
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16-4 Motion of a Charge in a Field
Deflection of Moving Charged Particles( electrons)
We can control the motion of a beam of charged
particles
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• ACT An electron beam moving horizontally at a
  speed V enters a region between two horizontally
  oriented plates of length L1. When the electrons
  reach a fluorescent screen located at a distance
  L2 past these plates, they have been deflected a
  vertical distance y from their original
  direction. If the speed of the electrons is
  doubled what is the new value of the deflection?

A) y/4 B) 4y C) 2y D) y E) y/2
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• ACT A ring of negative, uniform charge density
  is placed on the xz-plane with the center of the
  ring at the origin. A positive charge moves along
  the y axis toward the center of the ring. At the
  moment the charge passes through the center of
  the ring ________
• A) its velocity and its acceleration reach their
  maximum values.
• B) its velocity is maximum and its acceleration
  is zero.
• C) its velocity and its acceleration have
  non-zero values but neither is at its maximum.
• D) its velocity and its acceleration are both
  equal to zero.
• E) its velocity is zero and its acceleration is
  maximum.

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16-5 The Electric Dipole in an External Electric
Field
1. The motion of a dipole in an uniform external
electric field
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stable equilibrium
unstable equilibrium
A dipole in an uniform external electric field
only rotates
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2.The energy of a dipole in an external electric
field
We choose
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(a) 4, 3, 1, 2
(b) 3, the 1 and 4 tie, then 2
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(No Transcript)
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3. The motion of a dipole in an nonuniform
external electric field
A dipole placed in an nonuniform external
electric field experiences not only a net
force but also a torque.
The motion is a combination of linear
acceleration and rotation
We can explain the phenomena that a charged rod
can attracts small pieces of paper.
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• Act A neutral water molecule (H2O) in its vapor
  state has an electric dipole moment of magnitude

(a)  How far apart are the molecule's centers of
positive and negative charge
(b)  If the molecule is placed in an electric
field of , what maximum
torque can the field exert on it? (Such a field
can easily be set up in the laboratory.)
(c)  How much work must an external agent do to
turn this molecule end for end in this field,
starting from its fully aligned position, for
which q 0?
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Solution
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Summary of Chapter 16

• Electric field is defined as the force per unit
  charge

• Force on a point charge q

• Electric field lines are very useful for
  visualizing the electric field, as long as their
  limitations are taken into account.

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Summary of Chapter 16, cont.

• Electric field of a point charge

• Electric fields obey the superposition
  principle.
• Electric dipole equal and opposite charges
  separated by a distance L. The electric field is
  proportional to the dipole moment, which is

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Summary of Chapter16, cont.

• An electric dipole in an external electric field
  feels a torque, and has potential energy

• Electric field due to a continuous charge
  distribution