Vector Potential - HP 50g User Manual

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.,
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
, then function
The calculator provides function VPOTENTIAL, available through the command
catalog (‚N), to calculate the vector potential,
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., (x,y,z) = -x
It should be indicated that there is more than one possible vector potential
functions for a given vector field F. For example, the following screen shot
shows that the curl of the vector function
vector F =
(x,y,z) = (x,y,z)i+ (x,y,z)j+ (x,y,z)k, such that F = curl
(x,y,z) is referred to as the vector potential of F(x,y,z).
2 2
/2j + (-y /2+zx)k.
= [1-XY,2Z-1,ZY-2Y]. Application of function VPOTENTIAL
2
(x,y,z), given the vector
2 2 2
= [X +Y +Z ,XYZ,X+Y+Z] is the
1
F
=
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