Class 08: Outline
Hour 1:
Last Time: Conductors
Expt. 3: Faraday Ice Pail
Hour 2:
Capacitors & Dielectrics
P8- 1
Last Time:
Conductors
P8- 2
Conductors in Equilibrium
Conductors are equipotential objects:
1) E = 0 inside
2) Net charge inside is 0
3) E perpendicular to surface
4) Excess charge on surface
E =σ
ε0
P8- 3
Conductors as Shields
P8- 4
Hollow Conductors
Charge placed INSIDE induces
balancing charge INSIDE
+
- - +
+ - +
+q
+ -- - - +
+
+
P8- 5
Hollow Conductors
Charge placed OUTSIDE induces
charge separation on OUTSIDE
+q
-
-
+
E=0
+
+
P8- 6
PRS Setup
O2
I2
O1
I1
What happens
if we put Q in
the center?
P8- 7
PRS Questions:
Point Charge
Inside Conductor
P8- 8
Demonstration:
Conductive Shielding
P8- 9
Visualization: Inductive
Charging
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizatio
ns/electrostatics/40-chargebyinduction/40chargebyinduction.html
P8- 10
Experiment 3:
Faraday Ice Pail
P8- 11
Last Time:
Capacitors
P8- 12
Capacitors: Store Electric Energy
Q
C=
∆V
To calculate:
1) Put on arbitrary ±Q
2) Calculate E
3) Calculate ∆V
Parallel Plate Capacitor:
C=
ε0 A
d
P8-
Batteries &
Elementary Circuits
P8- 14
Ideal Battery
Fixes potential difference between its terminals
Sources as much charge as necessary to do so
Think: Makes a mountain
P8- 15
Batteries in Series
∆V1
∆V2
Net voltage change is ∆V = ∆V1 + ∆V2
Think: Two Mountains Stacked
P8- 16
Batteries in Parallel
Net voltage still ∆V
Don’t do this!
P8- 17
Capacitors in Parallel
P8- 18
Capacitors in Parallel
Same potential!
Q1
Q2
C1 =
, C2 =
∆V
∆V
P8- 19
Equivalent Capacitance
?
Q = Q1 + Q2 = C1∆ V + C2 ∆ V
= ( C1 + C2 ) ∆ V
Q
Ceq =
= C1 + C2
∆V
P8- 20
Capacitors in Series
Different Voltages Now
What about Q?
P8- 21
Capacitors in Series
P8- 22
Equivalent Capacitance
Q
Q
∆ V1 = , ∆ V2 =
C1
C2
∆ V = ∆ V1 + ∆ V2
(voltage adds in series)
Q
Q Q
∆V =
= +
Ceq C1 C2
1
1
1
= +
Ceq C1 C2
P8- 23
PRS Question:
Capacitors in Series and Parallel
P8- 24
Dielectrics
P8- 25
Demonstration:
Dielectric in Capacitor
P8- 26
Dielectrics
A dielectric is a non-conductor or insulator
Examples: rubber, glass, waxed paper
When placed in a charged capacitor, the
dielectric reduces the potential difference
between the two plates
HOW???
P8- 27
Molecular View of Dielectrics
Polar Dielectrics :
Dielectrics with permanent electric dipole moments
Example: Water
P8- 28
Molecular View of Dielectrics
Non-Polar Dielectrics
Dielectrics with induced electric dipole moments
Example: CH4
P8- 29
Dielectric in Capacitor
Potential difference decreases because
dielectric polarization decreases Electric Field!
P8- 30
Gauss’s Law for Dielectrics
Upon inserting dielectric, a charge density σ’ is
induced at its surface
G G
qinside (σ − σ ') A
=
w
∫∫ E ⋅ dA = EA =
S
ε0
ε0
What is σ’?
σ −σ '
E=
ε0
P8- 31
Dielectric Constant κ
Dielectric weakens original field by a factor κ
σ − σ ' E0 σ
E=
≡
=
ε0
κ κε 0
⇒
⎛ 1⎞
σ ' = σ ⎜1 − ⎟
⎝ κ⎠
Gauss’s Law with dielectrics:
Dielectric constants
Vacuum
1.0
free
3.7
inside Paper
Pyrex Glass 5.6
Water
80
0
G G q
d
κ
E
⋅
A
=
∫∫
S
ε
P8- 32
Dielectric in a Capacitor
Q0= constant after battery is disconnected
Upon inserting a dielectric: V =
V0
κ
Q0
Q0
Q
=κ
= κ C0
C= =
V V0 / κ
V0
P8- 33
Dielectric in a Capacitor
V0 = constant when battery remains connected
Q0
Q
C = = κ C0 = κ
V
V0
Upon inserting a dielectric:
Q = κ Q0
P8- 34
PRS Questions:
Dielectric in a Capacitor
P8- 35
Group: Partially Filled Capacitor
What is the capacitance of this capacitor?
P8- 36