1. The graded exams will be returned next Tuesday, Oct 4
The graded exams will be returned next Tuesday, Oct 4. You will have until the next class on Thursday, Oct 6 to rework the problems you got wrong and receive 50% added credit. Make sure you are in class as you will no have another opportunity to rework the exam. I will be going over the answers in class on Thursday. This will also be your only opportunity to ask for corrections/clarifications on any grading mistakes.
The homework assignment will be on line this afternoon but will not be due until Tuesday, Oct 11. This will give you the opportunity to start work on the problems so that you will not be overloaded with homework and the exam rework next week.

2. i.e. to separate charges and place them onto the opposite plates
Energy Storage in Capacitors
Electric Field Energy
Electric potential energy stored = amount of work done to charge the capacitor
i.e. to separate charges and place them onto the opposite plates
To transfer charge dq between
conductors, work dW=Vdq
Charged capacitor – analog to stretched/compressed spring
Capacitor has the ability to hold both charge and energy
Density of energy (energy/volume)
Energy is conserved in the E-field

3. Increased area, decreased separations, “stronger” insulators
In real life we want to store more charge at lower voltage, hence large capacitances are needed
Increased area, decreased separations, “stronger” insulators
Electronic circuits – like a shock absorber in the car, capacitor smoothes power fluctuations
Response on a particular frequency – radio and TV broadcast and receiving
Undesirable properties – they limit high-frequency operation

4. Example: Transferring Charge and Energy Between Capacitors
Switch S is initially open
What is the initial charge Q0?
What is the energy stored in C1?
After the switch is closed
what is the voltage across each
capacitor? What is the charge on each? What is the total energy? a) b)
c) when switch is closed, conservation of charge
Capacitors become connected in parallel d)
Where had the difference gone?
It was converted into the other forms of energy (EM radiation)

5. Definitions
Dielectric—an insulating material placed between plates of a capacitor to increase capacitance.
Dielectric constant—a dimensionless factor  that determines how much the capacitance is increased by a dielectric. It is a property of the dielectric and varies from one material to another.
Breakdown potential—maximum potential difference before sparking
Dielectric strength—maximum E field before dielectric breaks down and acts as a conductor between the plates (sparks)

6. Dielectrics have no free charges and they do not conduct electricity
Most capacitors have a non-conductive material (dielectric) between the conducting plates. That is used to increase the capacitance and potential across the plates.
Dielectrics have no free charges and they do not conduct electricity
Faraday first established this behavior

7. Capacitors with Dielectrics
Advantages of a dielectric include:
Increase capacitance
Increase in the maximum operating voltage. Since dielectric strength for a dielectric is greater than the dielectric strength for air
Possible mechanical support between the plates which decreases d and increases C.
To get the expression for anything in the presence of a dielectric you replace o with o

8. Field inside the capacitor became smaller – why?
We know what happens to the conductor in the electric field
Field inside the conductor E=0
outside field did not change
Potential difference (which is the
integral of field) is, however, smaller.
There are polarization (induced) charges
– Dielectrics get polarized

9. Properties of Dielectrics
Redistribution of charge – called polarization
dielectric constant of a material
We assume that the induced charge is directly
proportional to the E-field in the material
when Q is kept constant
In dielectrics, induced charges do not exactly
compensate charges on the capacitance plates

10. Induced charge density
Permittivity of the dielectric material
E-field, expressed through charge density s on the conductor plates
(not the density of induced charges) and permittivity of the dielectric
e (effect of induced charges is included here)
Electric field density in the dielectric
Example: A capacitor with and without dielectric
Area A=2000 cm2
d=1 cm; V0 = 3kV;
After dielectric is inserted, voltage V=1kV
Find; a) original C0 ; b) Q0 ; c) C d) K e) E-field

11. Dielectric Breakdown
Plexiglas breakdown
Dielectric strength is the maximum electric field the insulator can sustain before breaking down

12. Molecular Model of Induced Charge
Electronic polarization of nonpolar molecules

13. Electronic polarization of polar molecules
In the electric field more molecular dipoles are oriented along the field

14. Polarizability of an Atom
- separation of proton and electron cloud in the applied electric field
P- dipole moment per unit volume, N – concentration of atoms

15. Gauss’s Law in Dielectrics

16. Forces Acting on Dielectrics
We can either compute force directly
(which is quite cumbersome), or use
relationship between force and energy
Considering parallel-plate capacitor
Force acting on the capacitor, is pointed inside,
hence, E-field work done is positive and U - decreases
More charge here
x – insertion length
Two capacitors in parallel
w – width of the plates
constant force