Math 252 HW#07 sec. 4.5 #1 Maple Work

We start by loading the "linalg" package:

  with(linalg):

Example 4.9:

  A:=vector([A1,A2,A3]);

                          A := [A1, A2, A3]

  R:=vector([x,y,z]);

                            R := [x, y, z]

  G:=crossprod(A,R)/2;

           G := 1/2 [A2 z - A3 y, A3 x - A1 z, A1 y - A2 x]

  curl(G,[x,y,z]);

                             [A1, A2, A3]
This confirms that G is the vector potential for F = A.

Example 4.10:

  G:=1/3*crossprod(crossprod(A,R),R);

G := 1/3 [(A3 x - A1 z) z - (A1 y - A2 x) y,

    (A1 y - A2 x) x - (A2 z - A3 y) z,

    (A2 z - A3 y) y - (A3 x - A1 z) x]

  curl(G,[x,y,z]);

               [A2 z - A3 y, A3 x - A1 z, A1 y - A2 x]

  crossprod(A,R);

               [A2 z - A3 y, A3 x - A1 z, A1 y - A2 x]

  evalm(curl(G,[x,y,z])-crossprod(A,R));

                              [0, 0, 0]
This confirms that G is the vector potential for F = A x R.

SFU / Math & Stats / ~hebron / math252 / assignments / sol07 / maple / 4.5.1.html
Revised 22 March 1999 by John Hebron.