F07_hw06

# F07_hw06 - Physics 505 Homework Assignment#6 Due Thursday...

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Physics 505 Fall 2007 Homework Assignment #6 — Due Thursday, October 25 Textbook problems: Ch. 4: 4.1, 4.7, 4.8, 4.9 4.1 Calculate the multipole moments q lm of the charge distributions shown as parts a ) and b ). Try to obtain results for the nonvanishing moments valid for all l , but in each case ﬁnd the ﬁrst two sets of nonvanishing moments at the very least. a ) z a a q q q q - - a a x y b ) - a x y z q q a q 2 c ) For the charge distribution of the second set b ) write down the multipole expansion for the potential. Keeping only the lowest-order term in the expansion, plot the potential in the x - y plane as a function of distance from the origin for distances greater than a . d ) Calculate directly from Coulomb’s law the exact potential for b ) in the x - y plane. Plot it as a function of distance and compare with the result found in part c ). Divide out the asymptotic form in parts c ) and d ) to see the behavior at large distances more clearly. 4.7 A localized distribution of charge has a charge density

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F07_hw06 - Physics 505 Homework Assignment#6 Due Thursday...

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