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

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)

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

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

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”

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

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 +

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. -

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

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

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?

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