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Student[VectorCalculus]

  

ScalarPotential

  

compute the scalar potential of a vector field

 

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) calling sequence 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

withStudent[VectorCalculus]:

vVectorFieldx,y,z

v:=xe_x+ye_y+ze_z

(1)

ScalarPotentialv

12x2+12y2+12z2

(2)

Gradient

xe_x+ye_y+ze_z

(3)

vVectorFieldy,x,0

v:=ye_xxe_y

(4)

ScalarPotentialv

denx2+y2+z2

den:=x2+y2+z2

(5)

ScalarPotentialx,y,z→x,y,zden

x,y,z→12lnx2+y2+z2

(6)

SetCoordinatessphericalr,φ,θ

sphericalr,φ,θ

(7)

vVectorFieldr,0,0

v:=re_r

(8)

ScalarPotentialv

12r2

(9)

See Also

Student[VectorCalculus]

Student[VectorCalculus][Gradient]

Student[VectorCalculus][SetCoordinates]

Student[VectorCalculus][Vector]

Student[VectorCalculus][VectorField]

Student[VectorCalculus][VectorPotential]

 


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