VectorCalculus
ScalarPotential
Calling Sequence
Parameters
Description
Examples
ScalarPotential(v)
v
-
vector field or Vector valued procedure; specify the components of the vector field
The ScalarPotential(v) command computes the scalar potential of the vector field v. This is a function f such that Gradientf=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.
withVectorCalculus:
SetCoordinatescartesianx,y,z
cartesianx,y,z
v≔VectorFieldx,y,z
ScalarPotentialv
x22+y22+z22
v≔VectorFieldy,−x,0
ScalarPotentialx,y,z↦x,y,zx2+y2+z2
x,y,z↦lnx2+y2+z22
SetCoordinatessphericalr,φ,θ
sphericalr,φ,θ
v≔VectorFieldr,0,0
r22
Gradient
See Also
VectorCalculus[Gradient]
VectorCalculus[SetCoordinates]
VectorCalculus[Vector]
VectorCalculus[VectorField]
VectorCalculus[VectorPotential]
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