my office change was not reflected on the syllabus. it is now escn 2.206
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My office change was not reflected on the syllabus. It is now ESCN 2.206. Our first exam is a week from next Tuesday - Sep 27. It will cover everything I have covered in class including material covered next Thursday. - PowerPoint PPT PresentationTRANSCRIPT
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My office change was not reflected on the syllabus. It is now ESCN 2.206.
Our first exam is a week from next Tuesday - Sep 27. It will cover everything I have covered in class including material covered next Thursday.
There will be two review sessions Monday, Sep 26 - at 12:30 PM and at 3:00 PM in the same room as the problem solving session: FN 2.212.
I have put several (37) review questions/problems on Mastering Physics. These are not for credit but for practice. I will review them at the review session Monday.
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Example: Potential between oppositely charged parallel plates
From our previous examples
0( )
( )
U y q Ey
V y Ey
abVE
d
Easy way to calculate surface charge density
0 abV
d
Remember! Zero potential doesn’t mean the conducting object has no charge! We can assign zero potential to any place, only difference in potential makes physical sense
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Example: Charged wireWe already know E-field around the wireonly has a radial component
0
1;
2rEr
0
ln2
bb
aa
rE dr
r
Vb = 0 – not a good choice as it follows
Why so?
aV
We would want to set Vb = 0 at some distance r0 from the wire
0
0
ln2
rV
r
r - some distance from the wire
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Example: Sphere, uniformly charged inside through volume
3' r
q QR Q - total charge
Q
V - volume density of charge
( )r R r
R rR
E dr
eR
k Q
R
2
23
2e
rk Q r
R R
This is given that at infinity
rE03
R
R
2
3|
2re
R Rk Q r
R
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Potential Gradientb
a ba
E d l
We can calculate potential difference directlya
a bb
d
x y zE i E j E k E x y zd E dx E dy E dz
: :x y zE E Ex y z
Components of E in terms of
E operator "del"
Frequently, potentials (scalars!) are easier to calculate:
So people would calculate potential and then the field
Superposition for potentials: V = V1 + V2 + …
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Example: A positively charged (+q) metal sphere of radius ra is inside of another metal sphere (-q) of radius rb. Find potential at different pointsinside and outside of the sphere.
) : ) : )a a b ba r r b r r r c r r
+q
-q1
2
a) 2
0
10
( )4
( )4
b
a
qV r
r
qV r
r
Total V=V1+V2
0
1 1( )
4 a b
qV r
r r
b)
0
1 1( )
4 b
qV r
r r
c) 0V
Electric field between spheres Er
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Equipotential Surfaces
• Equipotential surface—A surface consisting of a continuous distribution of points having the same electric potential
• Equipotential surfaces and the E field lines are always perpendicular to each other
• No work is done moving charges along an equipotential surface
– For a uniform E field the equipotential surfaces are planes
– For a point charge the equipotential surfaces are spheres
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Equipotential Surfaces
Potentials at different points are visualized by equipotential surfaces (just like E-field lines).
Just like topographic lines (lines of equal elevations).
E-field lines and equipotential surfaces are mutually perpendicular
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Definitions cont
• Electric circuit—a path through which charge can flow
• Battery—device maintaining a potential difference V between its terminals by means of an internal electrochemical reaction.
• Terminals—points at which charge can enter or leave a battery
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Definitions
• Voltage—potential difference between two points in space (or a circuit)
• Capacitor—device to store energy as potential energy in an E field
• Capacitance—the charge on the plates of a capacitor divided by the potential difference of the plates C = q/V
• Farad—unit of capacitance, 1F = 1 C/V. This is a very large unit of capacitance, in practice we use F (10-6) or pF (10-12)
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Capacitors
• A capacitor consists of two conductors called plates which get equal but opposite charges on them
• The capacitance of a capacitor C = q/V is a constant of proportionality between q and V and is totally independent of q and V
• The capacitance just depends on the geometry of the capacitor, not q and V
• To charge a capacitor, it is placed in an electric circuit with a source of potential difference or a battery
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CAPACITANCE AND CAPACITORS
Capacitor: two conductors separated by insulator and charged by opposite and equal charges (one of the conductors can be at infinity)
Used to store charge and electrostatic energy
Superposition / Linearity: Fields, potentials and potential differences, or voltages (V), are proportional to charge
magnitudes (Q)
(all taken positive, V-voltage between plates)
Capacitance C (1 Farad = 1 Coulomb / 1 Volt) is determined by pure geometry (and insulator properties)
1 Farad IS very BIG: Earth’s C < 1 mF
QC
V
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Calculating Capacitance
1. Put a charge q on the plates
2. Find E by Gauss’s law, use a surface such that
3. Find V by (use a line such that V = Es)
4. Find C by
0encq
EAAdE
EssdEV
Vq
C
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Energy stored in a capacitor is related to the E-field between the plates Electric energy can be regarded as stored in the field itself.
This further suggests that E-field is the separate entity that may exist alongside charges.
Parallel plate capacitor
€
density σ = charge Q /area S
E =σ
ε0
=Q
ε0A; V = Ed =
Qd
ε0A
C =ε0A
d
Generally, we find the potential differenceVab between conductors for a certain charge Q
Point charge potential difference ~ Q
This is generally true for all capacitances
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Capacitance configurations
€
V = keQdr
r2a
b
∫ = keQ(1
ra
−1
rb
)
C =rarb
ke (rb − ra )
With rb →∞, C = ra /ke -
capacitance of an individual sphere
Cylindrical capacitor
)ln(2
)ln(22
ab
k
lC
a
b
l
Qk
r
drkV
e
e
b
a
e
Spherical Capacitance