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Student[VectorCalculus][VectorPotential] - compute the vector potential of a vector field in R^3
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Calling Sequence
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VectorPotential(v)
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Parameters
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v
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vector field or Vector-valued procedure; specify the components of the vector field in R^3
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Description
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The VectorPotential(v) calling sequence computes the vector potential of the vector field v. The result is a vector field F such that ![`&x`(VectorCalculus[Nabla], F) = v](/support/helpjp/helpview.aspx?si=4487/file05190/math45.png) . If a vector potential does not exist, NULL is returned.
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If v is a vector field, a vector field is returned. If v is a procedure, a procedure is returned.
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Examples
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![with(Student[VectorCalculus])](/support/helpjp/helpview.aspx?si=4487/file05190/math62.png)
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![v := Vector[column]([[y], [-x], [0]], ["x", "y", "z"], "field")](/support/helpjp/helpview.aspx?si=4487/file05190/math69.png)
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![Vector[column]([[-x*z], [-y*z], [0]], ["x", "y", "z"], "field")](/support/helpjp/helpview.aspx?si=4487/file05190/math76.png)
| (2) |
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![∇*RTABLE(18446790986281372118,MATRIX([[-x*z], [-y*z], [0]],["x", "y", "z"],"field"),Vector[column])](/support/helpjp/helpview.aspx?si=4487/file05190/math80.png)
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![Vector[column]([[y], [-x], [0]], ["x", "y", "z"], "field")](/support/helpjp/helpview.aspx?si=4487/file05190/math83.png)
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![SetCoordinates(cylindrical[r, theta, z])](/support/helpjp/helpview.aspx?si=4487/file05190/math87.png)
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![cylindrical[r, theta, z]](/support/helpjp/helpview.aspx?si=4487/file05190/math90.png)
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![v := Vector[column]([[r], [0], [-2*z]], ["r", "theta", "z"], "field")](/support/helpjp/helpview.aspx?si=4487/file05190/math97.png)
| (5) |
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^2*z-r*cos(theta)^2*z], [0]], ["r", "theta", "z"], "field")](/support/helpjp/helpview.aspx?si=4487/file05190/math104.png)
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![simplify(∇*RTABLE(18446790986281354294,MATRIX([[0], [-r*sin(theta)^2*z-r*cos(theta)^2*z], [0]],["r", "theta", "z"],"field"),Vector[column]))](/support/helpjp/helpview.aspx?si=4487/file05190/math108.png)
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![Vector[column]([[r], [0], [-2*z]], ["r", "theta", "z"], "field")](/support/helpjp/helpview.aspx?si=4487/file05190/math111.png)
| (7) |
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