compute a vector potential of a vector field in R^3 - Maple Help

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VectorCalculus[VectorPotential] - compute a vector potential of a vector field in R^3

Calling Sequence

VectorPotential(v)

Parameters

v

-

vector field or Vector valued procedure; specify the components of the vector field in R^3

Description

• 

The VectorPotential(v) command computes a vector potential of the vector field v.  The result is a vector field F such that ×F=v.  If a vector potential does not exist, NULL is returned.

• 

If v is a vector field, a vector field is returned.  If v is a procedure, a procedure is returned.

Examples

withVectorCalculus:

SetCoordinates'cartesian'x,y,z

cartesianx,y,z

(1)

v:=VectorFieldy,x,0

v:=ye_xxe_y

(2)

VectorPotentialv

xze_xyze_y

(3)

Curl

ye_xxe_y

(4)

SetCoordinates'cylindrical'r,θ,z

cylindricalr,θ,z

(5)

v:=VectorFieldr,0,2z

v:=re_r2ze_z

(6)

VectorPotentialv

rcosθ2zrsinθ2ze_θ

(7)

simplifyCurl

re_r2ze_z

(8)

See Also

VectorCalculus, VectorCalculus[CrossProduct], VectorCalculus[Curl], VectorCalculus[ScalarPotential], VectorCalculus[SetCoordinates], VectorCalculus[Vector], VectorCalculus[VectorField]


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