Wednesday, 6 July 2016
Charge 3 nC is in a hollow cavity
inside a large chunk of metal that is
electrically neutral. The total charge
29%
on the exterior surface
of the metal is
A. 0 nC.
B. +3 nC.
C. –3 nC.
D. Can’t say without
knowing the shape and
location of the hollow
cavity.
QuickCheck 27.15
Charge 3 nC is in a hollow cavity
inside a large chunk of metal that
is electrically neutral. The total
charge on the exterior surface
of the metal is
A. 0 nC.
B. +3 nC.
C. –3 nC.
D. Can’t say without knowing the shape
and location of the hollow cavity.
Slide 27-106
Example: cavity in conductor.
Charge on surface:
Q
Ф=0Q
encl=0
-Q
Q

Conducting shell around charge.
Induced charges on surfaces:
- +
+
-
+
Q
- +
-
Conducting shell around charge.
Induced charges on surfaces. Let’s say the conductor has
charge -3Q.
Q
inner
Q
outer
- +
 Q
+
+
 3Q  (Q)  2Q
Q
- +
-
Faraday Cages
Application:
The use of a conducting box, or Faraday cage, to
exclude electric fields from a region of space is called
screening.
07/06/2015
Oregon State University PH 213, Class #9
Slide 27-103
7
Surface charge.
Conductor:
Confusing words.
Thin conductor:
Q1=σiA
Q2=σiA
Q Q1  Q2
 
 2 i
A
A
Confusing words.
Thin conductor:
Surface or area charge density is twice the surface
or interface charge density.
Example (prob. 27.50, p. 808):
Two large, parallel conductive slabs, carrying net charges +Q
and +2Q, respectively, are located a distance l apart. The
slabs each have the same surface area, A (top + bottom; the
ends are thin enough to ignore).
In terms of Q and A…
a. Find the E-field strengths in each of five regions.
b. Find the surface charge densities on each of four surfaces.
07/06/2015
Oregon State University PH 213, Class #9
11
Slab vs plane with same charge Q
+++
y
+++
+++
y
+++
Chapter 28: Electric potential
• Potential
• Potential maps
• Potential in a capacitor
• Finding potential due to a charge distribution
Recall…
• Or more generally:
Uniform Fields
Two positive charges are
equal. Which has more
electric potential
energy?
29
A.Charge A.
B.Charge B.
C.They have the same
potential energy.
D.Both have zero potential
energy.
67 of 94
61%
QuickCheck 28.2
Two positive charges are
equal. Which has more
electric potential energy?
A.Charge A.
B.Charge B.
C.They have the same potential energy.
Increasing PE
D.Both have zero potential energy.
Slide 28-29
Two negative charges are
equal. Which has more
electric potential energy?
12%
A. Charge A.
B. Charge B.
C. They have the same
potential energy.
D. Both have zero
potential energy.
67 of 94
29
QuickCheck 28.3
Two negative charges are
equal. Which has more
electric potential energy?
A.
B.
C.
D.
Charge A.
Charge B.
They have the same potential energy.
Both have zero potential energy.
Increasing
PE for
negative
charge
Slide 28-34
Coulomb potential energy
Q
q
r
r   U  0
KQq
U
r
qQ
FK 2
r
Rank in order, from largest to smallest, the
potential energies Ua to Ud of these four
pairs of charges. Each + symbol represents
the same amount of charge.10%
29
68 of 95
A.
B.
C.
D.
E.
Ua = U b > Uc = Ud
Ub = Ud > Ua = Uc
U a = Uc > Ub = Ud
Ud > Uc > Ub > Ua
Ud > Ub = Uc > Ua
Rank in order, from largest to smallest, the
potential energies Ua to Ud of these four pairs
of charges. Each + symbol represents the
same amount of charge.
A.
B.
C.
D.
E.
Ua = Ub > Uc = U d
Ub = Ud > Ua = Uc
U a = U c > U b = Ud
U d > U c > U b > Ua
Ud > Ub = Uc > U a
Path independent
Q
q
r1
r2
 
U 2  U1    F  dl
2
1
r
qQ
FK 2
r
Potential
???
Potential
???
Potential
???
Potential: work per unit charge.
Analogue to gravity: work done proportional to mass:
U=mg
h
W=mg
h
U=0
h
Potential: work per unit charge.
Analogue to gravity: work done proportional to mass:
U=5mg
h
W=5mg
h
U=0
h
Potential: work per unit charge.
Analogue to gravity: work done proportional to mass:
V=gh
h
Potential: work per unit charge.
Electrical circuits can be quite complex:
V=V1
V=V2
V=V3
Device to increase potential
Gravity
Electricity
+
J/kg
J/C=V
When there is more than one path.
Potential diagrams:
6V
3.2V
+
-
0V
When there is more than one path.
Potential diagrams:
6V
3.2V
+
-
0V
When there is more than one path.
In the mountains:
Midterm Review
Conductors vs insulators
• Charge by induction
• Induced polarization
07/06/2015
Oregon State University PH 213, Class #9
38
Coulomb’s Law
• Point Charge
• Multiple Charges (incl. dipole)
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Oregon State University PH 213, Class #9
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Electric Field
• F=qE
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Oregon State University PH 213, Class #9
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Electric Flux
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Oregon State University PH 213, Class #9
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07/06/2015
Oregon State University PH 213, Class #9
42
Gauss’ Law
• The electric flux through any closed
surface equals (the net charge enclosed by
the surface)/ε0
07/06/2015
Oregon State University PH 213, Class #9
43
Gauss’ law
The Gauss’s Law Song
Walter Smith & Marian McKenzie 2-2-01
(To the tune of “East Side, West Side”)
Inside, outside, count the lines to tell –
If the charge is inside, there will be net flux as well.
If the charge is outside, be careful and you’ll see
The goings in and goings out are equal perfectly.
If you wish to know the field precise,
And the charge is symmetric,
you will find this law is nice –
Q upon a constant – eps’lon naught they say –
Equals closed surface integral of E dot n dA
07/06/2015
Oregon State University PH 213, Class #9
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