10   '
20   '           ELECTRIC POTENTIAL FOR A CHARGED WIRE
30   '
40   ' ----------------------- 4/14/93 --------------------------
50   '
60   ' -- This program calculates the electric potential for a charged
70   '    wire which is assumed to be a continuous finite line of charge.
80   '    The program finds the exact solution and approximate solutions
90   '    by Finite Sum, Trapezoidal Rule, and Simpson's Rule.
100  '
110  ' -- Thus four potential values are calculated:
120  '
130  '    V1 = Exact potential for the finite line of continuous charge
140  '    V2 = Approximation: Finite Sum from N point charges
150  '    V3 = Approximation: Trapezoidal Rule (another summing)
160  '    V4 = Approximation: Simpson's Rule: (another summing)
170  '
180  '           --> LIST OF PROCEDURES <--
190  '
200        GOSUB 310   'INITIALIZATIONS AND INPUT
210        GOSUB 500   'CALCULATE V1
220        GOSUB 580   'CALCULATE V2, V3, V4
230        GOSUB 1100  'OUTPUT
240        PRINT
250        PRINT
260        INPUT "WANT TO RUN ANOTHER (Y/N)? ", AGAIN$
270        IF AGAIN$ = "Y" OR AGAIN$ = "y" THEN 200
280        END
290  '
300  '------------------------------------------------------
310  'INITIALIZATIONS AND INPUT
320  '
330  'PRINT "INPUT VALUES FOR THE FOLLOWING:"
340  'PRINT "      NUMBER OF TERMS: N"
350  'PRINT "  HALF-LENGTH OF LINE: A"
360  'PRINT "    X CO-ORD OF POINT: X0"
370  'PRINT "    Y CO-ORD OF POINT: Y0"
     N = 101
     A = 1!
     X0 = 0!
     Y0 = 1!
     PRINT "          WAVE NUMBER: K"
380  PRINT
390  PRINT "SEPARATE THE VALUES WITH COMMAS AND PRESS RETURN"
400  PRINT
410  'INPUT N, A, X0, Y0, K
     INPUT K
420  '
430  ' -- We redefine N, making it the nearest larger odd integer.
440  ' -- This is really only necessary for Simpson's Rule,
450  '
460  N = 2 * INT(N / 2) + 1
470  '
480  RETURN
490  '------------------------------------------------------
500  'CALCULATE V1
510  '
520  V1N = SQR((X0 - A) ^ 2 + Y0 ^ 2) - (X0 - A)
530  V1D = SQR((X0 + A) ^ 2 + Y0 ^ 2) - (X0 + A)
540  V1 = LOG(V1N / V1D)
550  '
560  'RETURN
570  '------------------------------------------------------
580  'CALCULATE V2, V3, V4
590  '
600  ' -- V2, V3, and V4 are computed as sums over the number of
610  '    charges making up the line.  Set them initially to zero.
620  '
630  V2 = 0
640  V3 = 0
650  V4 = 0
660  '
670  ' -- DX is the spacing between adjacent point charges
680  '    used in the approximations
690  '
700  DX = 2 * A / (N - 1)
710  '
720  ' -- Start at one end of the line
730  '
740  X = -A
750  '
760  ' -- Loop to add the potential from each of N charges
770  '
780  FOR J = 1 TO N
790     '
800     ' -- L (for lambda) is the charge density (here assumed 1)
810     '
820     L = 1
830     '
840     ' -- F is the function we wish to integrate
850     '
860     F = L * COS(K * 3.14159 * X) / SQR((X - X0) ^ 2 + Y0 ^ 2)
870     '
880     ' -- Add contribution for Finite Sum
890     '
900     C = 1
910     V2 = V2 + C * F * DX
920     '
930     ' -- Add contribution for Trapezoidal Rule
940     '
950     IF J = 1 OR J = N THEN C = .5
960     IF J <> 1 AND J <> N THEN C = 1
970     V3 = V3 + C * F * DX
980     '
990     ' -- Add contribution for Simpson's Rule
1000    '
1010    IF J = 1 OR J = N THEN C = 1 / 3
1020    IF J = 2 * INT(J / 2) THEN C = 4 / 3
1030    IF J <> 1 AND J <> N AND J <> 2 * INT(J / 2) THEN C = 2 / 3
1040    V4 = V4 + C * F * DX
1050    X = X + DX
1060    NEXT J
1070 '
1080 RETURN
1090 '------------------------------------------------------
1100 'OUTPUT
1110 '
1120 PRINT
1130 INPUT "PRINTER (P) OR SCREEN (S)? ", ANS$
1140 IF ANS$ = "P" OR ANS$ = "p" THEN OPEN "LPT1:" FOR OUTPUT AS #1
1145 IF ANS$ = "S" OR ANS$ = "s" THEN OPEN "SCRN:" FOR OUTPUT AS #1
1150 IF ANS$ <> "P" AND ANS$ <> "p" AND ANS$ <> "S" AND ANS$ <> "s" THEN GOTO 1120
1160 '
1170 PRINT #1,
1180 PRINT #1, "N="; N, "   A="; A, "   X0="; X0, "   Y0="; Y0
1190 PRINT #1,
1200 PRINT #1, USING "V1 = #.##### "; V1
1210 PRINT #1, USING "V2 = #.##### "; V2
1220 PRINT #1, USING "V3 = #.##### "; V3
1230 PRINT #1, USING "V4 = #.##### "; V4
     PRINT #1, USING "V2-V4 = #.##### "; V2 - V4
     PRINT #1, USING "V3-V4 = #.##### "; V3 - V4
1240 '
1250 CLOSE #1
1260 '
1270 RETURN
1280 '---------------- END OF PROGRAM LINES ----------------