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Unformatted text preview: Physics 42 Homework From Tipler, 5th edition Instructions: Do all assigned problems. Please try to use the Method of Three Passes , attached. Read over this for other general comments and instructions in any event. Note that bonus questions have to be solved without the direct help of Kristine or me. You may still work in groups, you can solve them with discussion on the class list (where Kristine or I might reply to help out the entire class with our answers), you can ask other faculty or graduate students, you can look online or in other texts or in the library for solutions, but you have to build your problem solving skills and confidence by attacking them. They are often worth quite a lot of credit! Chapter 21: 41,47,56,61,62,72,78,81,85 Chapter 22: 29,47,50,56,61,66,77,88,92,93,94 Chapter 23: 16,59,73,85,87,88,89,90,91,92,93. Bonus questions, worth three points each: Find the potential of an electric dipole at an arbitrary point in space as follows. Put q at a/ 2 on the z-axis. Pick a point r = ( r,, = 0) (the latter just means in the plane of your picture). Write down the potential at that point. This is your answer. Now let r a . Do a binomial expansion of both denominators, set p a = qa , and tell me the potential of a point dipole at an arbitrary point in space relative to the dipole axis. Pretty cool! This is a really important thing to understand just ask Kristine! Problem 95. When you solve this you are actually deriving an important theorem that says that the potential at any point in space that is free from charge is the average over a spherical surface around that point. A related theorem tells you that both the maximum and minimum potential inside any charge-free volume must occur on the surface. Both of these are consequences of Gausss Law expressed as the Poisson equation (the inhomogeneous Laplace equation). You wont learn all of this for several years, but youll learn it much more easily then if you solve this problem now, which isnt that difficult! Chapter 24: 51, 56, 57, 84, 92, 93, 94, 97, 104, 112 Bonus: Problem 110. 1 Chapter 25: 30, 56, 57, 97, 116, 118, 133, 144, 145 Bonus. Suppose you have are handed a infinite flat piece of metal screen- ing consisting of thin wires in a rectangular mesh. Each bit of wire between two adjacent intersections in the screen has a resistance R . From symme- try, find the total resistance between to adjacent intersections. Note that this quantity is bound to be less than R because there are other pathways that current can take between the interactions. Note also that if you try to actually sum the resistance network, youll go mad. Theres a trick, so think about it and see if you can figure it out....
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