.MCAD 304020000 1 74 272 0
.CMD PLOTFORMAT
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 21 15 0 0 3 
.CMD PLOTFORMAT
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 21 15 0 1 3 
.CMD FORMAT  rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=0
.CMD SET ORIGIN 0
.CMD SET TOL 0.001000000000000
.CMD SET PRNCOLWIDTH 8
.CMD SET PRNPRECISION 4
.CMD PRINT_SETUP 1.200000 1.218750 1.200000 1.200000 0
.CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty*
.CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 colrid=16973856
.CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=16973856
.CMD DEFAULT_TEXT_PARPROPS 0 0 0
.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables
.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants
.CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text
.CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1
.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2
.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3
.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4
.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5
.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6
.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7
.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=2 family=Times^New^Roman points=12 bold=0 italic=1 underline=0 colrid=1
.CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD UNITS U=1
.CMD DIMENSIONS_ANALYSIS 0 0
.CMD COLORTAB_ENTRY 0 0 0
.CMD COLORTAB_ENTRY 128 0 0
.CMD COLORTAB_ENTRY 0 128 0
.CMD COLORTAB_ENTRY 128 128 0
.CMD COLORTAB_ENTRY 0 0 128
.CMD COLORTAB_ENTRY 128 0 128
.CMD COLORTAB_ENTRY 0 128 128
.CMD COLORTAB_ENTRY 128 128 128
.CMD COLORTAB_ENTRY 192 192 192
.CMD COLORTAB_ENTRY 255 0 0
.CMD COLORTAB_ENTRY 0 255 0
.CMD COLORTAB_ENTRY 255 255 0
.CMD COLORTAB_ENTRY 0 0 255
.CMD COLORTAB_ENTRY 255 0 255
.CMD COLORTAB_ENTRY 0 255 255
.CMD COLORTAB_ENTRY 255 255 255
.CMD COLORTAB_ENTRY 0 64 128
.TXT 3 2 266 0 0
Cg a72.000000,72.000000,28
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24\i \pard {\b\i0 COPYRIGHT MIRON 
KAUFMAN 1997}}
.TXT 4 19 120 0 0
Cg a34.625000,34.625000,53
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;\red0\green0\blue128;}{
\fonttbl{\f0\fcharset0\fnil Times New Roman;}{\f1\fcharset0\fnil 
Britannic Bold;}}\plain\cf1\fs24\i \pard {\cf2\f1\fs36\b\i0 Physics B 
PHY232/235\par Computer Project\par Laboratory #2b}{\cf2\f1\fs36\b 
\par }}
.TXT 13 -20 119 0 0
Cg a69.000000,69.000000,223
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24\i \pard {\i0 We calculate the 
electrostatic field E of a uniformly charged ring. The total charge is 
q and the radius is r.  The ring lies in the xy plane and the center 
is at (0,0,0). }{\i0 The potential V was obtained in file }{\b\ul\link1 
Phyblab2a.mcd}{\i0 .}}
.ATT
.ATT_END
.ATT
.LINK file:C:\WINMCAD\mirmcd\physics B\Phybla~1.mcd
.ATT_END
.EQN 11 4 2 0 0
{0:q}NAME:5*(10)^(-8)*{0:coul}NAME
.EQN 0 13 121 0 0
{0:r}NAME:0.5*{0:m}NAME
.EQN 1 11 130 0 0
{0:\e.0}NAME:8.85*(10)^(-12)*({0:farad}NAME)/({0:m}NAME)
.EQN 8 -26 81 0 0
{0:V}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME):(0&2*{0:\p}NAME`({0:q}NAME)/(8*({0:\p}NAME)^(2)*{0:\e.0}NAME)*(1)/(\((({0:x}NAME-{0:r}NAME*{0:cos}NAME({0:\q}NAME)))^(2)+(({0:y}NAME-{0:r}NAME*{0:sin}NAME({0:\q}NAME)))^(2)+({0:z}NAME)^(2)))&{0:\q}NAME)
.TXT 8 -2 225 0 0
Cg a72.000000,72.000000,256
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24\i \pard {\i0 To get the 
electric field we differentiate numerically V with respect to x, y and 
z.\par E}{\i0\dn x}{\i0  = -dV/dx, E}{\i0\dn y }{\i0 = -dV/dy,  E}{\i0
\dn z}{\i0  = -dV/dz.  It is less time consuming to first symbolicaly 
differentiate the integrant of V, and then to perform the integrations 
numerically.}}
.TXT 8 0 218 0 0
Cg b73.000000,73.000000,123
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24\i \pard {\i0 You can do this 
by copying the integrant of V; select the variable x; use 
Differentiate Under Variable from under Symbolic.}}
.EQN 6 2 219 0 0
(-1)/(16)*({0:q}NAME)/(({0:\p}NAME)^(2)*{0:\e.0}NAME*(((({0:x}NAME-{0:r}NAME*{0:cos}NAME({0:\q}NAME)))^(2)+(({0:y}NAME-{0:r}NAME*{0:sin}NAME({0:\q}NAME)))^(2)+({0:z}NAME)^(2)))^((3)/(2)))*(2*{0:x}NAME-2*{0:r}NAME*{0:cos}NAME({0:\q}NAME))
.TXT 9 -1 220 0 0
Cg a71.000000,71.000000,91
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs24\i 
\pard {\i0 After simplyfying by a factor of 2, putting the - sign, and 
integrating over }{\f1\i0 q}{\i0 , we get  E}{\i0\dn x}{\i0 :}}
.EQN 8 -1 221 0 0
{0:E.x}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME):(0&2*{0:\p}NAME`({0:q}NAME)/(8*({0:\p}NAME)^(2)*{0:\e.0}NAME)*({0}1)/((((({0:x}NAME-{0:r}NAME*{0:cos}NAME({0:\q}NAME)))^(2)+(({0:y}NAME-{0:r}NAME*{0:sin}NAME({0:\q}NAME)))^(2)+({0:z}NAME)^(2)))^((3)/(2)))*(
{0:x}NAME-{0:r}NAME*{0:cos}NAME({0:\q}NAME))&{0:\q}NAME)
.TXT 10 0 222 0 0
Cg a72.000000,72.000000,44
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24\i \pard {\i0 Similar formulas 
are obtained for E}{\i0\dn y}{\i0  and E}{\i0\dn z}{\i0 .}}
.EQN 6 0 223 0 0
{0:E.y}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME):(0&2*{0:\p}NAME`({0:q}NAME)/(8*({0:\p}NAME)^(2)*{0:\e.0}NAME)*({0}1)/((((({0:x}NAME-{0:r}NAME*{0:cos}NAME({0:\q}NAME)))^(2)+(({0:y}NAME-{0:r}NAME*{0:sin}NAME({0:\q}NAME)))^(2)+({0:z}NAME)^(2)))^((3)/(2)))*(
{0:y}NAME-{0:r}NAME*{0:sin}NAME({0:\q}NAME))&{0:\q}NAME)
.EQN 13 0 224 0 0
{0:E.z}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME):(0&2*{0:\p}NAME`({0:q}NAME)/(8*({0:\p}NAME)^(2)*{0:\e.0}NAME)*({0}1)/((((({0:x}NAME-{0:r}NAME*{0:cos}NAME({0:\q}NAME)))^(2)+(({0:y}NAME-{0:r}NAME*{0:sin}NAME({0:\q}NAME)))^(2)+({0:z}NAME)^(2)))^((3)/(2)))*
{0:z}NAME&{0:\q}NAME)
.TXT 10 0 261 0 0
Cg a73.000000,73.000000,36
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24\i \pard {\i0 The magnitude of 
the electric field:}}
.EQN 7 1 258 0 0
{0:E}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME):\(({0:E.x}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME))^(2)+({0:E.y}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME))^(2)+({0:E.z}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME))^(2))
.TXT 6 -1 262 0 0
Cg a70.000000,70.000000,52
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24\i \pard {\i0 First we get the 
electric field vs x for y = z = 0m.}}
.EQN 5 7 235 0 0
{0:x}NAME:-1.03*{0:m}NAME,-0.99*{0:m}NAME;1.03*{0:m}NAME
.EQN 0 25 236 0 0
{0:y}NAME:0.*{0:m}NAME
.EQN 0 14 237 0 0
{0:z}NAME:0*{0:m}NAME
.EQN 8 -43 232 0 0
5000&-5000&(_n_u_l_l_&_n_u_l_l_)&({0:E.x}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME))/((({0:volt}NAME)/({0:m}NAME))),({0:E.y}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME))/((({0:volt}NAME)/({0:m}NAME))),({0:E.z}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME))/((({0:volt}NAME)/(
{0:m}NAME)))@1&-1&(_n_u_l_l_&_n_u_l_l_)&({0:x}NAME)/({0:m}NAME)
0 1 1 1 1 0 0 1 1 
0 1 1 1 1 0 0 1 1 
1 1 0 0 1 1 NO-TRACE-STRING
2 1 1 0 1 1 NO-TRACE-STRING
3 1 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 54 28 10 0 3 
.TXT 61 -2 271 0 0
Cg a72.000000,72.000000,28
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24\i \pard {\b\i0 COPYRIGHT MIRON 
KAUFMAN 1997}}
.TXT 4 2 239 0 0
Cg a70.000000,70.000000,73
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24\i \pard {\i0 Next we get the 
electric field vs z for x = y = 0m, i.e. the ring's axis.}}
.EQN 3 4 240 0 0
{0:x}NAME:0*{0:m}NAME
.EQN 0 25 241 0 0
{0:y}NAME:0.*{0:m}NAME
.EQN 0 14 242 0 0
{0:z}NAME:-1*{0:m}NAME,-0.9*{0:m}NAME;1*{0:m}NAME
.EQN 1 -43 243 0 0
1000&-1000&(_n_u_l_l_&_n_u_l_l_)&({0:E.x}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME))/((({0:volt}NAME)/({0:m}NAME))),({0:E.y}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME))/((({0:volt}NAME)/({0:m}NAME))),({0:E.z}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME))/((({0:volt}NAME)/(
{0:m}NAME)))@1&-1&(_n_u_l_l_&_n_u_l_l_)&({0:z}NAME)/({0:m}NAME)
0 1 1 1 1 0 0 1 1 
0 1 1 1 1 0 0 1 1 
1 1 0 0 1 1 NO-TRACE-STRING
2 1 1 0 1 1 NO-TRACE-STRING
3 1 3 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 54 28 10 0 3 
.TXT 38 -3 245 0 0
Cg a70.000000,70.000000,172
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24\i \pard {\i0 Finally we show 
the electric field vs y for fixed x and y.  Note that now the three 
components of the E vector are nonzero. We also calculate the 
magnitude of the E vector.}}
.EQN 5 4 246 0 0
{0:x}NAME:0.25*{0:m}NAME
.EQN 0 25 247 0 0
{0:y}NAME:-1.03*{0:m}NAME,-0.98*{0:m}NAME;1.03*{0:m}NAME
.EQN 0 24 250 0 0
{0:z}NAME:0.1*{0:m}NAME
.EQN 3 -53 249 0 0
_n_u_l_l_&_n_u_l_l_&(_n_u_l_l_&_n_u_l_l_)&({0:E.x}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME))/((({0:volt}NAME)/({0:m}NAME))),({0:E.y}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME))/((({0:volt}NAME)/({0:m}NAME))),({0:E.z}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME))/((({0:volt}NAME)
/({0:m}NAME))),({0:E}NAME({0:x}NAME,{0:y}NAME,{0:z}NAME))/((({0:volt}NAME)/({0:m}NAME)))@1&-1&(_n_u_l_l_&_n_u_l_l_)&({0:y}NAME)/({0:m}NAME)
0 1 1 1 1 0 0 1 1 
0 1 1 1 1 0 0 1 1 
1 1 0 0 1 1 NO-TRACE-STRING
2 1 1 0 1 1 NO-TRACE-STRING
3 1 3 0 1 1 NO-TRACE-STRING
0 1 5 0 3 3 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 54 35 10 0 3 
.TXT 50 1 272 0 0
Cg a72.000000,72.000000,28
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24\i \pard {\b\i0 COPYRIGHT MIRON 
KAUFMAN 1997}}