Physics 212 Lecture 4, Slide 1

1
Physics 212 Lecture 4
Today's Concept Gauss Law Applied to
Determine E field in cases of sufficient symmetry

2
Overview

• Prelecture 4
• Use Gauss Law to determine fields for
  symmetrical charge distributions
• 3-Dimensions Spherical Symmetry Uniformly
  charged solid sphere
• 2-Dimensions Cylindrical Symmetry Infinite
  solid cylindrical conductor
• 1-Dimension Planar symmetry Infinite
  sheet of charge
• Superposition Two infinite sheets of charge
• Lecture Plan
• Review difficulties
• Electric fields and charge distributions in
  conductors
• Review preflights
• Do Gauss Law calculation
• E field
• Charge distribution

3
Index
Preflight 1
Guess the Field
Preflight 2
Calculation
Difficulties
Game Hit The Cake
Preflight 7,8,9
Music
Summary
Extra 3
Extra 4
Extra 5
4
Summary

• What have we learned?

5
Preflight 1
BACK
D
E
6
Preflight 2
B
A
C
D
E
7
.
a
Preflight 2
-q
q
A) Ea
B) Ea
C) Ea0

• The net field is outward at this point because
  the positive sphere points radially outward and
  the negative field points inward itself giving
  once more an outward net field.
• I would assume that the negative charged
  conducting sphere would overpower the more
  distant positive charged conducting sphere making
  it point radially inward.
• The total enclosed charge is zero, so the
  electric field is zero outside of the spheres

BACK
D
E
8
Preflight 3
B
D
A
C
BACK
9
Which of the following field line pictures best
represents the electric field from two charges
that have the same sign but different magnitudes?
A
B
C
D
BACK
10
Difficulties
Claim E 0 inside any conductor at equilibrium

• Why?
• At equilibrium, the charges inside conductor are
  not moving
• If charges inside conductor are not moving, the
  force on any charge is zero
• If the force on any charge inside the conductor
  is zero, the electric field (E F/q) must also
  me zero

-q
SIMULATION 1
2q
Claim Excess charge on conductor only on surface
at equilibrium

• Why?
• Apply Gauss Law
• Take Gaussian surface to be just inside
  conductor surface

BACK
SIMULATION 2
11
Calculation
y
neutral conductor
r2
Point charge 3Q at center of neutral conducting
shell of inner radius r1 and outer radius r2. a)
What is E everywhere?
3Q
r1
x
First question Do we have enough symmetry to
use Gauss Law to determine E? Yes..
Spherical Symmetry (what does this mean???)
BACK
12
y
Calculation
Point charge 3Q at center of neutral conducting
shell of inner radius r1 and outer radius r2. a)
What is E everywhere?
neutral conductor
r2
We know magnitude of E is fcn of r
direction of E is along
3Q
r1
x
13
y
Calculation
Point charge 3Q at center of neutral conducting
shell of inner radius r1 and outer radius r2. a)
What is E everywhere?
neutral conductor
r2
We know
3Q
r1
x
r lt r1
r gt r2
r1 lt r lt r2
14
y
Calculation
-Q

• Suppose give conductor a charge of -Q
• What is E everywhere?
• What are charge distributions at r1 and r2?

r2
conductor
3Q
r1
x
r gt r2
A B C
BACK
15
Pre-flight 7
Briefly explain why the electric field inside a
conductor is zero.
A
The charge in a conductor is zero because a
conductor does not allow charge to move inside of
it, and the charge in that sphere must be uniform
throughout at radius R, and if there was a charge
anywhere in the sphere, the sphere would clearly
not be uniform throughout.
B
The charges in a conductor are free to move. If
there is a field inside the conductor, the
charges will experience a net force and move.
Therefore if the charges are in a static
equilibrium, then the field must inside the
conductor must be 0.
C
Because a conductor allows electrons to travel
along its outside surface with least resistance.
D
Im not sure.
BACK
16
Pre-flight 8
The fact that the electric field inside a
conductor is zero implies that any net charge on
the conductor must exist only on the surface.
Describe why this is consistent with Gauss Law.
This works with Gauss' Law because in order for
Gauss' Law to work, the electric field must be
constant and uniform. By moving the charges to
the surface of an object, this is true.
A
B
Gausses law takes the integral of the dot product
of the electrical field and the area, not volume.
C
One could draw a Gaussian surface just in side
the conductor and since the electric field is
zero, Gauss' Law says there must be no enclosed
charge. Thus all of the charge must be on the
surface of the conductor.
D
Im not sure.
BACK
17
Pre-flight 9
The fact that the electric field inside a
conductor is zero implies that any net charge on
the conductor must exist only on the surface.
Describe why this is consistent with Coulombs
Law.
Since the charges have the same sign they repel
each other according to Coulombs law. This
results in the charges being pushed to the edges
of a conductor.
BACK
18
Do positive charges move in a real metal
conductor ? No, but
The net result of this can be viewed in two
equivalent ways
19
Do positive charges move in a real metal
conductor ? No, but
The net result of this can be viewed in two
equivalent ways
And
20
Do positive charges move in a real metal
conductor ? No, but
The net result of this can be viewed in two
equivalent ways
And
21
Music

• Who is the Artist?
• Susan Tedeschi
• Marcia Ball
• Shawn Colvin
• Bonnie Raitt
• Melissa Etheridge

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Ad Lib 2
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Ad Lib 3
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Ad Lib 4
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25
Ad Lib 5
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