HP 48gII Graphing Calculator Manual do Utilizador descarregar pdf (Página 477)

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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

/2j + (-y

/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

= [X

,XYZ,X+Y+Z] is the

vector F = ∇× Φ

= [1-XY,2Z-1,ZY-2Y]. Application of function VPOTENTIAL

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HP 48gII Graphing Calculator Manual do Utilizador Página 477

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