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## Homework 1

E&M, Fall '10, Homework 1 (due Friday Sept. 10, 9:30 AM, in class)

1. In class Wednesday we found that two balls separated by a meter would exert forces of one Newton on each other if each had a charge of 10

2. Consider the "classical" model of the Hydrogen atom: an electron in a circular orbit around a proton. (Note that the proton is much heavier than the electron, so it will basically stay fixed in space just as the Sun stays basically fixed while the much lighter planets orbit it.) The radius of an atom is about half an Angstrom -- that is, .5 * 10

3. Problem 43 from the book ("earth and moon")

4. Imagine an infinitely long and perfectly straight wire with a certain amount of electric charge uniformly distributed over its length. That is, assume there is a constant charge per unit length "lambda" on the wire. Now suppose there is a little ball with electric charge Q a distance R from the wire. Calculate the force exerted on the ball by the wire. (This will require using calculus. Start by developing an expression for the relevant component of the force produced by some one random little piece of the wire, then integrate to add up the contributions from all the little pieces composing the wire.)

1. In class Wednesday we found that two balls separated by a meter would exert forces of one Newton on each other if each had a charge of 10

^{-5}Coulombs. Estimate the fraction of such a ball's electrons that would have to be removed in order to give it this much charge.2. Consider the "classical" model of the Hydrogen atom: an electron in a circular orbit around a proton. (Note that the proton is much heavier than the electron, so it will basically stay fixed in space just as the Sun stays basically fixed while the much lighter planets orbit it.) The radius of an atom is about half an Angstrom -- that is, .5 * 10

^{-10}meters. What speed must the electron move with to maintain a circular orbit of this radius? What is its orbital period around the proton?3. Problem 43 from the book ("earth and moon")

4. Imagine an infinitely long and perfectly straight wire with a certain amount of electric charge uniformly distributed over its length. That is, assume there is a constant charge per unit length "lambda" on the wire. Now suppose there is a little ball with electric charge Q a distance R from the wire. Calculate the force exerted on the ball by the wire. (This will require using calculus. Start by developing an expression for the relevant component of the force produced by some one random little piece of the wire, then integrate to add up the contributions from all the little pieces composing the wire.)

Last modified: Monday, December 19, 2011, 9:18 AM