317 (F96) Final Exam

317 (F96) Final Exam - 7########,############### #########

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Unformatted text preview: 7########,############### ######### ########z##################D##q##D##q###############.##############(##( #"##J####f####f#P###x######.# ##N#### #*###*###########J##f#m####L##i#####=###################### ####Name 1. [40 points total] A spherical dielectric of radius R has a uniform polarization # frozen in.A. [4 points] What are the units of the constant k?B. [12 points] Find sb and rb. Show your work.C.[16 points] Integrate over the bound charge distribution to find the monopole moment, Q, and the dipole moment, #, for the sphere. Show your work. You should know the answers before you start, but perform the integrations anyway.D. [8 points] Use the multipole expansion to find the approximate force (magnitude and direction) exerted by the sphere on a point charge q located at Cartesian coordinates #(20R, 0, 0). Show your work.2. [30 points total] If the charge density of the electron cloud in a neutral atom is modeled by the density function, #, where Qe is the total charge of the electron cloud and a is the radius of the cloud, then the dipole moment induced in the atom would not be linearly related to the external electric field causing the polarization. In this case the dipole moment for the atom would take the form: #A. [18 points] Find a and b. Show your work.B. [12 points] A point charge q is located a large distance s away from such a neutral atom. Find the force of attraction between them. Show your work. (Note: If you did not find an answer to part A, just leave your answer to this part in terms of a and b.) 3. (GRE problem) We have learned that many dielectrics respond to an external electric field # with a polarization that is proportional to and in the same direction as #. In such dielectrics, the total electric field, # , within the dielectric is smaller than the external # by a constant factor K (known as the dielectric constant). In other words, # [15 points] A dielectric of dielectric constant K is placed in contact with a large conducting plate having surface charge density s. What is the polarization (bound) charge density sp on the surface between the two materials? A. # B. # C. # D. # E. # Show your work to justify your choice.Name Total Points Name Total Points Physics 317 (Fall 1996) Fourth Exam (November 22, 1996)#v###v##5)####8#########"###*###########"#########"###d##xpr####### ## ### #######",## #MT Extra# # .#####*## #####"###"## ###currentpoint #"###### #(#####r ,#####Times#####(####P ,# ###Symbol#####) #=#####) #k# ##(#####) #####(####z ###30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1088 div 480 3 -1 roll exch div scale currentpoint translate 64 63 translate 69 26 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /MT-Extra f1 (r) show 6 353 moveto 384 /Times-Italic f1 (P) show 337 353 moveto...
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This document was uploaded on 10/29/2011 for the course PHSX 317 at MSU Bozeman.

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317 (F96) Final Exam - 7########,############### #########

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