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Student[VectorCalculus]

  

VectorPotential

  

compute the vector potential of a vector field in R^3

 

Calling Sequence

Parameters

Description

Examples

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 CurlF=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

withStudentVectorCalculus:

vVectorFieldy,x,0

vye_x+xe_y+0e_z

(1)

VectorPotentialv

xze_x+yze_y+0e_z

(2)

ye_x+xe_y+0e_z

(3)

SetCoordinatescylindricalr,θ,z

cylindricalr,θ,z

(4)

vVectorFieldr,0,2z

vre_r+0e_θ+2ze_z

(5)

VectorPotentialv

0e_r+rcosθ2zrsinθ2ze_θ+0e_z

(6)

re_r+0e_θ+2ze_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]