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1P8-
Class 08: Outline
Hour 1:Last Time: ConductorsExpt. 3: Faraday Ice Pail
Hour 2:Capacitors & Dielectrics
2P8-
Last Time:Conductors
3P8-
Conductors in Equilibrium
Conductors are equipotential objects:1) E = 0 inside2) Net charge inside is 03) E perpendicular to surface 4) Excess charge on surface
0εσ=E
4P8-
Conductors as Shields
5P8-
Hollow Conductors
Charge placed INSIDE induces balancing charge INSIDE
+q-- -
-
++
+
-
-- -
--
-+
+
++ +
6P8-
Hollow Conductors
Charge placed OUTSIDE induces charge separation on OUTSIDE
+q
---
-
+
+
+E=0
7P8-
PRS Setup
I1
I2O1
O2What happens if we put Q in the center?
8P8-
PRS Questions:Point Charge
Inside Conductor
9P8-
Demonstration:Conductive Shielding
10P8-
Visualization: Inductive Charging
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/electrostatics/40-chargebyinduction/40-chargebyinduction.html
11P8-
Experiment 3:Faraday Ice Pail
12P8-
Last Time:Capacitors
P8-
Capacitors: Store Electric Energy
QCV
=∆
To calculate:1) Put on arbitrary ±Q 2) Calculate E3) Calculate ∆V
Parallel Plate Capacitor:
0 ACdε
=
14P8-
Batteries & Elementary Circuits
15P8-
Ideal Battery
Fixes potential difference between its terminalsSources as much charge as necessary to do so
Think: Makes a mountain
16P8-
Batteries in Series
∆V1 ∆V2
Net voltage change is ∆V = ∆V1 + ∆V2
Think: Two Mountains Stacked
17P8-
Batteries in Parallel
Net voltage still ∆VDon’t do this!
18P8-
Capacitors in Parallel
19P8-
Capacitors in Parallel
Same potential!
1 21 2,Q QC C
V V= =∆ ∆
20P8-
Equivalent Capacitance
?
( )1 2 1 2
1 2
Q Q Q C V C VC C V
= + = ∆ + ∆
= + ∆
1 2eqQC C CV
= = +∆
21P8-
Capacitors in Series
Different Voltages NowWhat about Q?
22P8-
Capacitors in Series
23P8-
Equivalent Capacitance
1 21 2
Q QV , VC C
∆ = ∆ =
1 2V V V∆ = ∆ + ∆(voltage adds in series)
1 2eq
Q Q QVC C C
∆ = = +
1 2
1 1 1
eqC C C= +
24P8-
PRS Question:Capacitors in Series and Parallel
25P8-
Dielectrics
26P8-
Demonstration:Dielectric in Capacitor
27P8-
DielectricsA dielectric is a non-conductor or insulatorExamples: rubber, glass, waxed paper
When placed in a charged capacitor, the dielectric reduces the potential difference between the two plates
HOW???
28P8-
Molecular View of Dielectrics
Polar Dielectrics : Dielectrics with permanent electric dipole moments Example: Water
29P8-
Molecular View of Dielectrics
Non-Polar DielectricsDielectrics with induced electric dipole momentsExample: CH4
30P8-
Dielectric in Capacitor
Potential difference decreases because dielectric polarization decreases Electric Field!
31P8-
Gauss’s Law for Dielectrics
Upon inserting dielectric, a charge density σ’ is induced at its surface
0S
insideqd EAε
⋅ = =∫∫ E A0
'εσσ −
=E( )0
' Aσ σε−
=
What is σ’?
32P8-
Dielectric Constant κDielectric weakens original field by a factor κ
0
0 0
' EE σ σ σε κ κε−
= ≡ = 1' 1σ σκ
⎛ ⎞= −⎜ ⎟⎝ ⎠
⇒
Gauss’s Law with dielectrics:
0S
freeinsideqdκε
⋅ =∫∫ E A
Dielectric constantsVacuum 1.0Paper 3.7Pyrex Glass 5.6Water 80
33P8-
Dielectric in a CapacitorQ0= constant after battery is disconnected
0VVκ
=Upon inserting a dielectric:
0 00
0 0/Q QQC C
V V Vκ κ
κ= = = =
34P8-
Dielectric in a CapacitorV0 = constant when battery remains connected
Upon inserting a dielectric: 0Q Qκ=
00
0
QQC CV V
κ κ= = =
35P8-
PRS Questions:Dielectric in a Capacitor
36P8-
Group: Partially Filled Capacitor
What is the capacitance of this capacitor?