HP 48gII - Manual (Page 477)

Page 15-6
As an example, in an earlier example we attempted to find a potential
function for the vector field F(x,y,z) = (x+y)i + (x-y+z)j + xzk, and got an error
message back from function POTENTIAL. To verify that this is a rotational
field (i.e.,
∇×F ≠ 0), we use function CURL on this field:
On the other hand, the vector field F(x,y,z) = xi + yj + zk, is indeed
irrotational as shown below:
Vector potential
Given a vector field F(x,y,z) = f(x,y,z)i+g(x,y,z)j+h(x,y,z)k, if there exists a
vector function
Φ(x,y,z) = φ(x,y,z)i+ψ(x,y,z)j+η(x,y,z)k, such that F = curl Φ =
∇× Φ, then function Φ(x,y,z) is referred to as the vector potential of F(x,y,z).
The calculator provides function VPOTENTIAL, available through the
command catalog (
‚N), to calculate the vector potential, Φ(x,y,z), given
the vector field, F(x,y,z) = f(x,y,z)i+g(x,y,z)j+h(x,y,z)k. For example, given
the vector field, F(x,y,z) = -(yi+zj+xk), function VPOTENTIAL produces
i.e.,
Φ(x,y,z) = -x 2 /2j + (-y 2 /2+zx)k.
It should be indicated that there is more than one possible vector potential
functions
Φ for a given vector field F. For example, the following screen shot
shows that the curl of the vector function Φ
1
= [X 2 +Y 2 +Z 2 ,XYZ,X+Y+Z] is the
vector F = ∇× Φ
2
= [1-XY,2Z-1,ZY-2Y]. Application of function VPOTENTIAL