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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "PHYSICS RESOURCE PACKETS P
ROJECT                               File: CSPHERE.MWS" }}{PARA 0 "" 
0 "" {TEXT -1 110 "Rose-Hulman Institute of Technology                \+
                       Authors: Perry Peters & Greg Williby" }}{PARA 
0 "" 0 "" {TEXT -1 97 "http://www.rose-hulman.edu/~moloney            \+
                       Software: Maple V Release 4" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 546 "The electric field betwe
en 2 concentric spheres is E=Q/(4pi eo r^2). where Q is the charge on \+
the inner sphere of radius A. Plot the capacitance of these spheres (l
et the radius of the smaller sphere be 0.25 m) as a function of the ra
dius of the outer sphere. In the limit as this radius goes to infinity
 this might be called the capacitance of a single sphere. (This is lik
e being asked to put one hand behind your back and clap.) Can you do t
he same limiting calculation for flat plates or for cylinders? [No, on
ly works for concentric spheres]" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 8 "Solution" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Equation for ele
ctric field between the two spheres" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
32 "Efield:=q/(4*Pi*epsilon[0]*r^2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 130 "The capacitance of these two spheres is C=q/dV, where dV is th
e change in potential of the two spheres.  Find dV by integrating E." 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "dV:=int(Efield,r=R1..R2);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Thus C is:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "Cap:=simplify(q/dV);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 69 "Plot the capacitance as a function of the radius of the o
uter sphere." }}{PARA 0 "" 0 "" {TEXT -1 47 "In order to do this, Eo a
nd R1 must be defined." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "epsilon[0
]:=8.854*10^(-12);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "R1:=.2
5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "plot(Cap*10^9,R2=0.25
..3,C=0..1/2,numpoints=200,title=`Capacitance (nF) as a function of R2
`);" }}}}{MARK "0 0 0" 79 }{VIEWOPTS 1 1 0 1 1 1803 }