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VectorCalculus

  

VectorPotential

  

compute a vector potential of a vector field in R^3

 

Calling Sequence

Parameters

Description

Examples

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)

vVectorFieldy,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)

vVectorFieldr,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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