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

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Student[VectorCalculus][VectorPotential] - compute the 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) calling sequence computes the vector potential of the vector field v.  The result is a vector field F such that ×F=v (that is, the curl of F is the field 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

withStudent[VectorCalculus]:

v:=VectorFieldy,x,0

v:=ye_xxe_y

(1)

VectorPotentialv

xze_xyze_y

(2)

Curl

ye_xxe_y

(3)

SetCoordinatescylindricalr,θ,z

cylindricalr,θ,z

(4)

v:=VectorFieldr,0,2z

v:=re_r2ze_z

(5)

VectorPotentialv

rcosθ2zrsinθ2ze_θ

(6)

simplifyCurl

re_r2ze_z

(7)

See Also

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


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