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?