{VERSION 4 0 "IBM INTEL NT" "4.0" }
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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "# Program to Illustr
ate two charged rings being moved away from the origin symmetrically;
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "#   At the moment .. bo
th rings are charged the same" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 20 "restart;with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
60 "v:=1000*q/sqrt( (x-a)^2 + R^2);# Electric potential function" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "Ex:=simplify(-diff(v,x)); # \+
Electric field in the x direction" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 87 "a1:=4; b:=-a1; # A1 is the magnitude of the distance \+
away from the origin for each ring" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 90 "e2rings:=subs(q=+1,a=a1,R=3*sqrt(2),Ex)+subs(q=+1,a=b
,R=3*sqrt(2),Ex);  #add the two rings" }}}{PARA 11 "" 1 "" {TEXT -1 0 
"" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "e2ringsa:=subs(q=+1,a=a
1,R=3*sqrt(2),Ex); # field from \"right\" ring " }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 65 "e2ringsb:=subs(q=+1,a=b,R=3*sqrt(2),Ex); # fie
ld from \"left\" ring" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 194 "p
lot([e2ringsa,e2ringsb,e2rings],x=-15..15,view=-50..50,labels=[\"x\",
\"E\"],color=[yellow,blue,green],thickness=[2,2,4]);  # plot with blue
=left, yellow=right, green=combined field  - expanded view" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "plot([e2ringsa,e2ringsb,e2rings],x
=-5..5,view=-50..50,labels=[\"x\",\"E\"],color=[yellow,blue,green],thi
ckness=[2,2,4]);  # view zoomed around the origin" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 72 "fsolve(\{e2rings=0\},\{x\},\{x=-8..-0.0001\}
); #solve for the zero on the left" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "fsolve(
\{e2rings=0\},\{x\},\{x=-0.0001..0.0001\}); # verify the zero in the m
iddle (if equal q's)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "fso
lve(\{e2rings=0\},\{x\},\{x=0.0001..8\}); #solve for zero on the right
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "17" 0 }
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