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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "PHYSICS RESOURCE PACKETS P
ROJECT                               File: CIRCLOOP.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 -1 354 "A circular loop of wire \+
of radius  R is centered at the origin in the x-y plane and carries a \+
current I counterclockwise from the x-axis to the y-axis.  Perform an \+
integration using the Biot-Savart law to determine the magnetic field \+
components (Bx,By,Bz) at a point (0,0,H) due to half of the loop --- t
hat half of the loop where x is greater than zero." }}{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 "" {MPLTEXT 1 
0 13 "with(linalg):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "Vector to \+
point in 3d space." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "P:=vector([0,
0,H]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 29 "Vector to point on wire loop." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 41 "s:=vector([R*cos(theta),R*sin(theta),0]);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 27 "Direction around wire loop." }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 22 "ds:=map(diff,s,theta);" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 29 "Vector from loop to 3d point." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "r:=evalm(P-s);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
15 "Biot-Savart law" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "dB:=mu[0]*i*
crossprod(ds,r)/(4*Pi*sqrt(dotprod(r,r))^3);" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 60 "Distribute constant over the three components of the ve
ctor." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "dBvect:=evalm(dB);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "Integrate around half loop to find
 B." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "solsymb:=map(int,dBvect,thet
a=-Pi/2..Pi/2);" }}}}{MARK "0 0 0" 2 }{VIEWOPTS 1 1 0 1 1 1803 }