PHYS351-tst2-Spring2006

# PHYS351-tst2-Spring2006 - ~" Dr Gangopadhyaya S'e I...

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Unformatted text preview: ~ '" Dr. Gangopadhyaya S'e:. I V--~OV\ Test II Physics 351 March 29, 2006 As always, to receive full credit you must show your work in a neat, organized and a legible form. 1. Laplace's Eq.jspherical:Thecharge density on a sphere of radius R is given by (j = (jo(l + cos B). (a) Determine the potential V(r, B) in the region r < Rand r > R. (b) Determine radial and angular components of the electric field at a point described by its spherical coor- dinates (2R, ~,1f). bot , ' 1\ ~ 2 r. LD.P,(J)) p~ (Uf?O) V ~. ~ L rR4\ jl 'i ~ \~ ~ ';:: L a~ r ok BVt-"1 , \- ~ [ :0 0-° , (H tAr> 0) ~ 'I d-Y ~o ~>(t Y~tl ~ ~o- ~'2. f:r ()Ir CD \0, (1\ ~:: R2 aLRt = 61 )z ~~ \ ( V,'~:C v~)--CD ~ 'poc ~D)-t!Q ~ (C#1(Q) ~ Gv-w =-.1-1-- )<2- r ~Q ) b L =- fw Q ;> 1.. rLj2 ) b }. OR =0 \0 J. It tz?,., I.:, VI.. , I- , 0.-\. 2. Q I12. '5- 0°, ~. , ~(L ,- 6~ V,, Y':: CO,,{< l~-t3~ C-t'?9 J . ~ eo .. 3> o.,~, E'""- ~ E""- J.. ~ V 'f 0"') (9 'V 'Of;>. .', Eo;t::: <JoJ22.. [- .3-.. . 2u-:,o r. 1 8~-1. ~- , ,9-2- [ D-- ~~«) J eo Y '.? Y' '? j e '< co 3 y-l- " r;;t-- 1- <1"£. Af, =- <j'b 'Jj?! 60?" lj ~ 6.£0 D6 [ 1-) r; :[ Q. a.. ~ + ~-t)) h ,. J Py. \0l1i) 1~ R~~ ~ ~ (bo '" ~ [l ' , 2 Go /' ~O ...- Foy ~H o~ ~ R~ I ..,. Ri-t1 aD..:: avO(- Go 1-\ RR 1-+ ,- R-l.-r'L l~~) <"" " A-+) J ~,V\fJL-- «'I.- ~'2.- ~ Ci,::i<ro eo rr- 'S b ~.L vJ I 3 eo, ~ \/6-v---I = (f'(>~ 2- \' .1. -t , C;\1;. D R ) 6'0 l ~ sV'-"- !JJr' ;g; 1:/2- ~:J!...
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PHYS351-tst2-Spring2006 - ~" Dr Gangopadhyaya S'e I...

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