1. Capacitors Q D
A capacitor is a device that is capable of storing electric charges and thus electric potential energy.
=> charging
Its purpose is to release them later in a controlled way.
=> discharging
Capacitors are used in vast majority of electrical and electronic devices. +Q -Q
Typically made of two conductors and, when charged, each holds equal and opposite charges.

2. Polar and Nonpolar Dielectrics
Polar dielectrics: dielectric material whose molecules have permanent electric dipole moments, such as water.
Eext = 0: the orientations of the permanent electric dipoles are distributed randomly, so the net dipole moment of the material is zero.
Eext  0 : the molecular dipoles try to align themselves with the field against random thermal motion, resulting in a net dipole moment.
Nonpolar dielectrics: molecules with no permanent electric dipole moments.
Eext  0 :  charges separate, induced dipole moment emerges.
Show the first demo:5A-31

3. Dielectrics between Capacitor Plates
+ Q
- Q
free charges
Electric field E between plates can be calculated from Q – q.
neutral -q +q
The presence of a dielectric weakens the electric field, therefore weaken the potential drop between the plates, and leads to a large capacitance.

4. Inserting Dielectrics (= Insulator)
Inserting a dielectric between the plates of a capacitor increases capacitance
Q=CV
holds more charges at fixed V
Dielectric constant  of a dielectric is the ratio of the capacitance when filled with it to that without it:
 > 1 always (dimensionless)
Material 
air (1 atm)
paper
3.7
pyrex
5.6
water (20C)
80.4
strontium titanate
310
Under the same Q,
V = V0/k
E = E0/k
Show demo: 5A-30.
Dielectric strength: breakdown field per unit length
Breakdown potential determined by dielectric strength (Emax)

5. Capacitors in Parallel
V is common
Equivalent Capacitor:
where

6. Capacitors in Series
q is common
Equivalent Capacitor:
where 

7. Conductor inserted between plates
A parallel-plate capacitor with conductor inserted in the middle
Two capacitors of area A in series -Q a b +q -q +q a b a -q +q -q
E=0 outside capacitors
E=0 in conductor
between plates
between plates
(a)

8. Warm-up quiz
All the capacitors have the same capacitance C, What is the total capacitance?
A). 4/3 C
B). 3/4 C
C). 3/2 C
D). 1/2 C
E). 2/3

9. Non-uniform Parallel-plate Capacitor 1
Equivalent to 2 capacitors in parallel
Potential drop V in each is the same.
Note if
even though a

10. Non-uniform Parallel-plate Capacitor 2
Equivalent to 2 capacitors in series
(Free) charge in each Q is the same.
Note if +Q -Q +Q
addition of the “animated” metal plate has no effect on the field in 1/4d and 3/4d since the field produced by +Q and –Q are cancelled -Q

11. Inserting Dielectric Material with Battery Disconnected
Charge a parallel plate capacitor filled with air (or vacuum) to potential difference V0.
Deposits charge Q
2. Disconnect the battery
Q remains fixed -Q
3. Insert a dielectric of dielectric constant  Q
So, V and E decreases from V0 , E0 to
and -Q
and

12. Inserting Dielectric Material with Battery Connected
Charge a parallel plate capacitor filled with vacuum (air) to potential difference V.
Deposits charge
2. Keep the battery connected
V remains fixed
3. Insert a dielectric of dielectric constant 
So, Q increases from Q0 and E remains fixed
and
and

13. Force between the plates of a capacitor
What is the force between these charged plates? +Q -Q
Battery disconnected
Is it attractive?
Yes!
Is it ?
Not quite!
Force F acting on a charge q in the electric field E created by other source charges is given by:
E created by the charge on the upper plate at the location of the lower plate is

14. Energy stored in a capacitor revisited+Q -Q
Battery disconnected
separation  0 +Q -Q
separation  d
External work required to separate the plates from zero to d m apart is
When d = 0, Volume=0, i.e. U = 0
This is also the potential energy stored in capacitor.
What if a battery remains connected?

15. Force and energy with battery connected, a mystery?
Force between plates? +Q -Q
Battery connected V
attractive
Work to change separation from 0 to d? 
separation  0 +Q -Q
Q changes
separation  d
separation d+d
separation  d
However,

16. Lecture quiz A.
Five identical capacitors have the same capacitance C. Then capacitor (e) is filled with a material with dielectric constant k. What is the total capacitance? a b e c d
A). 2C
B). 1/(1+k) C
C). (1+k)C
D). 5 C
E). [4/(4+k)] C

17. Lecture quiz B.
Five identical capacitors have the same capacitance C. Then capacitor (e) is filled with a material with dielectric constant k. What is the total capacitance? a b e c d
A). 2C
B). [k/(1+k)] C
C). (1+k)C
D). [1/(1+k)] C C
E). (4+k) C

18. Lecture quiz C.
Four identical capacitors have the same capacitance C. Then capacitor (a) is filled with a material with dielectric constant k. What is the total capacitance? a b c d
A). (3/2 + k) C
B). (3+k) C
C). 5/2 C
D). (2/3 +k) C
E). (3+k) C