Solid conducting sphere with charge Q A E r V r A

Ionization and corona discharge There is maximum potential to which a conductor in air can be raised because of ionization. Small potentials applied to sharp points in air produce sufficiently high fields just outside the point to ionize the surrounding air.

The metal mast at the top of the Empire State Building acts as a lightning rod. It is struck by lightning as many as 500 times each year. A lightning rod has a sharp end so that lightning bolts will pass through a conducting path in the air that leads to the rod; a conducting wire leads from the lightning rod to the ground.

Benjamin Franklin

"For my own part I wish the Bald Eagle had not been chosen the Representative of our Country. He is a Bird of bad moral Character. He does not get his Living honestly. You may have seen him perched on some dead Tree near the River, where, too lazy to fish for himself, he watches the Labour of the Fishing Hawk; and when that diligent Bird has at length taken a Fish, and is bearing it to his Nest for the Support of his Mate and young Ones, the Bald Eagle pursues him and takes it from him. "With all this Injustice, he is never in good Case but like those among Men who live by Sharping & Robbing he is generally poor and often very lousy. Besides he is a rank Coward: The little King Bird not bigger than a Sparrow attacks him boldly and drives him out of the District. He is therefore by no means a proper Emblem for the brave and honest Cincinnati of America who have driven all the King birds from our Country.... "I am on this account not displeased that the Figure is not known as a Bald Eagle, but looks more like a Turkey. For the Truth the Turkey is in Comparison a much more respectable Bird, and withal a true original Native of America... He is besides, though a little vain & silly, a Bird of Courage, and would not hesitate to attack a Grenadier of the British Guards who should presume to invade his Farm Yard with a red Coat on." --Benjamin Franklin, in a letter to his daughter

Current, Ohm’s Law, Etc.

where R is resistance Resistance does not vary with the applied voltage resistor

Experimentally it is found that R depends on the material the wire is made of and its dimensions. Does not depend on the shape. In a wire of uniform resistivity and cross sectional area, the electric field is a constant for constant currents.

+ - V

Exercise 1 Given the resistivity of copper, about Ohm-m, what length of 0.5 cm diameter wire will yield a resistance of 10 Ohms?

Can you make a light bulb work with a battery and a wire? “Minds of Our Own” by Dr. Matthew H. Schneps and Dr. Philip M. Sadler Harvard-Smithsonian How can students graduate from prestigious schools like Harvard or MIT and not know even some of the most basic ideas in science taught in grade school?

Current Density Consider current flowing in a homogeneous wire with cross sectional area A.

The Continuity Equation for Steady State Currents Currents and current densities are constant in time – steady state. The flux of out of any closed surface must be zero.

Another form of Ohm’s Law

For steady state situation

Metal: ρ increases with increasing T Resistivity and temperature

Semiconductors: ρ decreases with increasing T

Superconductor Once a current has been established in a superconducting ring, it continues indefinitely without the presence of any driving field Dutch physicist Heike Kamerlingh Onnes - Hg 2003

Water NitrogenOxygen Boils Freezes 100 C (212 F)-196 C (-322 F)-183 C (-297 F) 0 C (32 F) -210 C (-346 F) -223 C (-369 F) Our air is ¾ Nitrogen and ¼ Oxygen

1908- liquefied helium produced First discovered in mercury by Kamerlingh-Onnes in Critical temperature 4.21K. Nobel Prize in Superconductivity

High-T c Superconductivity Liquid nitrogen temperature 77 K Complex ceramic materials were discovered in They exhibit superconductivity at much higher temperatures – above LN temperature! Muller and Bednortz, Nobel Prize 1987

Meissner effect and magnetic levitation

Current, Ohm’s Law, Etc.

The Continuity Equation for Steady State Currents Currents and current densities are constant in time – steady state. The flux of out of any closed surface must be zero.

For steady state situation

Problem 4 Two wires having different resistivities ρ 1 and ρ 2 and equal cross sections, a, are connected end to end. Their lengths are l 1 and l 2. If a battery is connected to this system such that a potential difference of V is maintained between the ends, a)What will be the current densities in the wires? b) What will be the potential difference across each wire? c)Will there be any charge on the surface where the wires are connected?

Exercise 5 Consider a cylindrical shell, inner radius a and outer radius b. It is made of material with resistivity ρ. Suppose a current can be made to flow out from the inner surface to the outer. What would the resistance be for this current?

For steady state situation 1.Kirchhoff’s junction rule: The algebraic sum of the currents into any junction is zero. 2.Kirchhoff’s loop rule: The algebraic sum of the potential differences in any loop must be zero.