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VectorCalculus

  

ScalarPotential

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ScalarPotential(v)

Parameters

v

-

vector field or Vector valued procedure; specify the components of the vector field

Description

• 

The ScalarPotential(v) command computes the scalar potential of the vector field v.  This is a function f such that ∇f=v.  If a scalar potential does not exist, NULL is returned.

• 

If v is a Vector field, an algebraic expression is returned. If v is a Vector-valued procedure, a procedure is returned.

Examples

withVectorCalculus:

SetCoordinates'cartesian'x,y,z

cartesianx,y,z

(1)

vVectorFieldx,y,z

v:=xe_x+ye_y+ze_z

(2)

ScalarPotentialv

12x2+12y2+12z2

(3)

vVectorFieldy,x,0

v:=ye_xxe_y

(4)

ScalarPotentialv

ScalarPotentialx,y,z→x,y,zx2+y2+z2

x,y,z→12lnx2+y2+z2

(5)

SetCoordinates'spherical'r,φ,θ

sphericalr,φ,θ

(6)

vVectorFieldr,0,0

v:=re_r

(7)

ScalarPotentialv

12r2

(8)

Gradient

re_r

(9)

See Also

VectorCalculus

VectorCalculus[Gradient]

VectorCalculus[SetCoordinates]

VectorCalculus[Vector]

VectorCalculus[VectorField]

VectorCalculus[VectorPotential]

 


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