HP (Hewlett-Packard) 50g ユーザーズマニュアル

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:

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