Student[VectorCalculus]
ScalarPotential
compute the scalar potential of a vector field
Calling Sequence
Parameters
Description
Examples
ScalarPotential(v)
v
-
vector field or Vector-valued procedure; specify the components of the vector field
The ScalarPotential(v) calling sequence 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.
withStudentVectorCalculus:
v≔VectorFieldx,y,z
ScalarPotentialv
x22+y22+z22
Gradient
v≔VectorFieldy,−x,0
den≔x2+y2+z2
ScalarPotentialx,y,z↦x,y,zden
x,y,z↦lnx2+y2+z22
SetCoordinatessphericalr,φ,θ
sphericalr,φ,θ
v≔VectorFieldr,0,0
r22
See Also
Student[VectorCalculus][Gradient]
Student[VectorCalculus][SetCoordinates]
Student[VectorCalculus][Vector]
Student[VectorCalculus][VectorField]
Student[VectorCalculus][VectorPotential]
Download Help Document