1. Question 300 V/m 0 V/m 300 V/m A B 0.02m 0.03m 0.04m What is VB-VA?D
What is VB-VA?
270 V
-270 V
-18 V
6 V
-6 V

2. Question
0 V/m A B
0.02m
0.03m
0.04m x D
VB-VA = -300*(0.02-0) - (-300)*( )=-6+12 V = +6 V

3. Potential in Metal Not in static equilibrium
Metal is not in static equilibrium:
When it is in the process of being polarized
When there is an external source of mobile charges (battery)
Nonzero electric field of uniform magnitude E throughout the interior of a wire of length L.
Direction of the field follows the direction of the wire.
For each step, the potential difference is: V = -EL
But in a circuit a thick copper wire may have a very small electric field. B is at lower potential than A.

4. Electric Field and Potential
If we know electric field ( ) everywhere we can compute potential (V) in every point in space.
Can we compute ( ) if we know V?

5. Exercise
Suppose in some area of space V(x,y,z)=x2+yz. What is E(x,y,z)?

6. Wire in a Circuit and Electric Field
In a current-carrying wire in a circuit, there can be a nonzero electric field, so there is a difference in potential between two locations in the wire.
Electric field is not confined to wire in a circuit – there is E around!
Electric field is not confined to the wire in a circuit – there must be an electric field E around the wire in the air!

7. Potential of a Uniformly Charged RingQ
Method 1: Divide into point charges and add up contributions due to each charge

8. Potential of a Uniformly Charged RingQ
Method 2: Integrate electric field along a path
Note that we integrate from an initial z=infinity to a final z so that V represents the energy per unit charge required to move a point charge in from infinity to z.

9. Potential of a Uniformly Charged RingQ
What is V for z>>R ?
Is it unexpected?
The same as for a point charge!

10. The difference between metals and insulators+Q -Q
insulator
metal -Q +Q
E inside insulator
is non zero
E inside metal =

11. Dielectric Constant
Electric field in capacitor filled with insulator: Enet=Eplates-Edipoles -Q +Q -q +q - +
qdipoles = b*Q
Alpha is small.
K – dielectric constant

12. Dielectric Constant Inside an insulator:
Dielectric constant for various insulators:
vacuum 1 (by definition)
air
typical plastic 5
NaCl 6.1
water 80
strontium titanate 310

13. Potential Difference in a Capacitor with Insulator
demonstration s

14. Potential Difference in Partially Filled CapacitorK -Q +Q
Talk if time permits – skip with no consequences. Note that we ignore the electric field due to the dielectric in the vacuum region. s A B x

15. Finding Potential Difference
1. Subtract the potential at the initial location A from the potential at final location B A B
2. Travel along a path from A to B adding up at each step: A B E dl

16. Common Pitfall
Assume that the potential V at a location is defined by the electric field at this location. A
Example: E = 0 inside a charged metal sphere, but V is not!

17. A negative test charge Q = -0
A negative test charge Q = -0.6C was moved from point A to point B In a uniform electric field E=5N/C. The test charge is at rest before and after the move. The distance between A and B is 0.5m and the line connecting A and B is perpendicular to the electric field. How much work was done by the net external force while moving the test charge from A to B? A B
0.5m
E = 5 N/C
1.5J 0J
–1.5J
3.0J
–3.0J

18. After moving the -0.6C test charge from A to B, it was then moved from B to C along the electric field line. The test charge is at rest before and after the move. The distance between B and C also is 0.5m. How much work was done by the net external force while moving the test charge from A to C? A C B
0.5m
E = 5 N/C
1.5J 0J
–1.5J
3.0J
-3.0J
1.5 J

19. Instead of moving the test charge from A to B then to C, it is moved from A to D and then back to C. The test charge is at rest before and after the move. How much work was done by the net external force while moving the test charge this time?
E = 5 N/C A B
0.5m C D
1.5J 0J
–1.5J
Infinitely big
Do not know at this time.

20. Conducting charged sphere and concentric charged conducting shellrA rB rC Q1 Q2
A solid conducting sphere of radius rA has charge Q1 uniformly distributed over its surface. Concentric with the solid sphere is a conducting shell of inner radius rB and outer radius rC with charge Q2 on its outer surface. What is the electric potential at the center of the solid sphere? Take the potential at infinity to be equal to zero and the origin at the center of the solid sphere.

21. Energy Density of Electric Field
How much work do I need to do to increase separation of plates?
Wby_you=Fby_you*s
Note that by doing so you increase area in space where electric field
(E = Q/A0) is present.
(for small s)

22. Energy Density of Electric Field
Energy can be stored in electric fields
Multiply by A/A and 0/0 E
Volume
in which we created electric field
Until now we have thought of energy (potential energy) as associated with interacting charges
Move one plate of a capacitor.
Field energy density:
(J/m3)
Formula holds for any charge configuration.
Energy expended by us was converted into energy stored in the electric field

23. Potential Energy and Field Energy
A different way to express
instead of calculating a work it takes to assemble charges.
all space
The idea of energy stored in fields is a general one:
Magnetic and gravitational fields can also carry energy.

24. An Electron and a Positron
System
Surroundings e+ e-
Release electron and positron – the electron (system) will gain kinetic energy
Conservation of energy  surrounding energy must decrease
Does the energy of the positron decrease?
- No, it increases
Where is the decrease of the energy in the surroundings?
- Energy stored in the fields must decrease

25. An Electron and a Positron
System
Surroundings e+ e-
Energy:
Single charge:
Dipole:
Can in principle integrate: run into problem – E is infinity close to the charge!
(far)
Energy stored in the E fields decreases as e+ and e- get closer!