1. Equipotential Lines Are Topographical Maps
Regions of high potential are like “mountains”
For positive charges, they have a lot of energy there
Regions of low potential are like “valleys”
For positive charges, they have minimum energy there
Electric fields point down the slope
Closely spaced equipotential lines means big electric field

2. Conductors and Batteries
A conductor has zero electric field inside it
Therefore, conductors always have constant potential
A wire is a thin, flexible conductor: circuit diagram looks like this:
A switch is a wire that can be connected or disconnected
open switch
closed switch
A battery or cell is a device that creates a fixed potential difference
The circuit symbol for a battery looks like this:
The long side is at higher potential
It is labeled by the potential difference
1.5 V
The potential difference E across the battery is called electromotive force (emf)

3. Conducting Spheres
Given the charge q on a conducting sphere of radius R, what is the potential everywhere?
Outside the sphere, the electric field is the same as for a point charge
Therefore, so is the potential
Inside, the potential is constant
It must be continuous at the boundary q R

4. Sample Problem q1 q2
Two widely separated conducting spheres, of radii R1 = 1.00 cm and R2 = 2.00 cm, each have 6.00 nC of charge put on them. What is their potential? They are then joined by an electrical wire. How much charge do they each end up with, and what is the final potential?
After connections, their potentials must be equal

5. Electric Fields near conductors
The potential for the two spheres ended up the same
The electric fields at the surface are not the same q1 q2
The more curved the surface is, the higher the electric field is there
Very strong electric field here
A sharp point can cause charged particles to spontaneously be shed into air, even though we normally think of air as an insulator.
Called “Corona discharge”

6. The Millikan Oil Drop experiment
Atomizer produced tiny drops of oil; gravity pulls them down
Atomizer also induces small charges
Electric field opposes gravity
If electric field is right, drop stops falling -
Millikan showed that you always got integer multiples of a simple fundamental charge

7. The Lightning Rod
Rain drops “rubbing” against the air can cause a separation of charge
This produces an enormous electric field
If electric field gets strong enough, it can cause breakdown of atmosphere +
Put a pointy rod on top of the building you want to protect
Coronal discharge drains away the charge near the protected object
Lightning hits somewhere else +

8. The Van de Graff Generator
Hollow conducting sphere, insulating belt, source of electric charge
Source causes charge to move to the belt
Belt rotates up inside sphere
Charge jumps to conductor inside sphere
Charge moves to outside of sphere
Since all the charge is on the outside of the sphere, process can be repeated indefinitely. -

9. Electrostatic Precipitator
Hollow conducting tube with a thin wire hanging down inside it
Dirty air enters at the bottom
Coronal discharge from wire produces lots of O2- ions
O2- ions hit dust particles, giving them charge
Charged dust now flows towards walls
Clean gas flows out the top
Gravity (shaking helps) causes dust to fall to the bottom of the container
Clean air
50 kV
Dirty air

10. Capacitors and Dielectrics
Conductors are commonly used as places to store charge
You can’t just “create” some positive charge somewhere, you have to have corresponding negative charge somewhere else
Definition of a capacitor:
Two conductors, one of which stores charge +Q, and the other of which stores charge –Q. –Q +Q b a
V
Can we relate the charge Q that develops to the voltage difference V?
Gauss’s Law tells us the electric field between the conductors:
Integration tells us the potential difference

11. Capacitance
The relationship between voltage difference and charge is normally linear
This allows us to define capacitance
Capacitance has units of Coulomb/Volt
Also known as a Farad, abbreviated F
A Farad is a very large amount of capacitance
Let’s work it out for concentric conducting spheres:
What’s the capacitance of the Earth, if we put the “other part” of the charge at infinity?

12. Parallel Plate Capacitors
A “more typical” geometry is two large, closely spaced, parallel conducting plates
Area A, separation d.
Let’s find the capacitance:
Charge will all accumulate on the inner surface
Let + and – be the charges on each surface
As we already showed using Gauss’s law, this means there will be an electric field given by:
If you integrate the electric field over the distance d, you get the potential difference A d
Circuit symbol for a capacitor:
To get a large capacitance, make the area large and the spacing small