Joule losses

1) A resistor as a resistance of 100kilohms and a power rating of one-quarter watt. What is the maximum voltage that can be applied across it?

Energy

A copper atom contains 29 electrons, one of which is a conduction electron. Copper has an atomic weight of 64 and a density of 8.9 x 10^3 kilograms/meter^3. Suppose that you have two copper spheres, each one having a volume of 1 centimeter^3. The spheres are depleted of their conduction electrons and separated by a distance of 100 millimeters. a.Calculate the force of repulsion. Show that this force is equal to about 0.5% of the force of attraction between the sun and earth. b.Calculate the energy stored in one sphere. That is the energy required to remove the conduction electrons. c.How much would this energy cost, at 10 cents per kilowatt-hour? d.To obtain this energy, y... click for more

Resistive film

A square film of Nichrome, an alloy of nickel and chromium, has copper electrodes deposited on two opposite edges. Show that the resistance between the electrodes depends only on the thickness of the film on its conductivity, as long as the film is square. This surface resistance is expressed in ohms per square.

Quadrupole and octupole terms of a dipole

1) A single point charge Q is at P'(0,0,s). First expand its potential at point P forms an angle theta with the z-axis, and r >> s. The distance from Q to P is r'. Disregard terms of the order (s/r)^4 and higher. Write out the values of V1, V2, V3. 2) Calculate V for a dipole exactly, a identify the quadrupole and octupole terms. The octupole term varies as (s/r)^4. You can disregard terms in (s/r)^5, (s/r)^6, etc.

Electric Fields

1) Draw electric field lines for a quadrupole formed of charges +Q, -Q, +Q, -Q at the corners of a square. Charges on a diagonal have the same sign. (On a field line, dy/dx = Ey/Ex)