vectorPotential

Vector potential of vector field

Syntax

vectorPotential (V, X)

vectorPotential(V)

Description

vectorPotential(V,X)computes thevector potential of the vector fieldVwith respect to the vectorXin Cartesian coordinates. The vector fieldVand the vectorXare both three-dimensional.

example

vectorPotential(V)returns the vector potentialVwith respect to a vector constructed from the first three symbolic variables found inVbysymvar.

Examples

Compute Vector Potential of Field

Compute the vector potential of this row vector field with respect to the vector[x, y, z]:

syms x y z vectorPotential([x^2*y, -1/2*y^2*x, -x*y*z], [x y z])

ans = -(x*y^2*z)/2 -x^2*y*z 0

Compute the vector potential of this column vector field with respect to the vector[x, y, z]:

syms x y z f(x,y,z) = 2*y^3 - 4*x*y; g(x,y,z) = 2*y^2 - 16*z^2+18; h(x,y,z) = -32*x^2 - 16*x*y^2; A = vectorPotential([f; g; h], [x y z])

A(x, y, z) = z*(2*y^2 + 18) - (16*z^3)/3 + (16*x*y*(y^2 + 6*x))/3 2*y*z*(- y^2 + 2*x) 0

Test if Vector Potential Exists for Field

To check whether the vector potential exists for a particular vector field, compute the divergence of that vector field:

syms x y z V = [x^2 2*y z]; divergence(V, [x y z])

ans = 2*x + 3

If the divergence is not equal to 0, the vector potential does not exist. In this case,vectorPotentialreturns the vector with all three components equal toNaN:

vectorPotential(V, [x y z])

ans = NaN NaN NaN

Input Arguments

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`V`—Vector field
3-D symbolic vector of symbolic expressions or functions(default)

Vector field, specified as a 3-D vector of symbolic expressions or functions.

`X`—Input
vector of three symbolic variables

Input, specified as a vector of three symbolic variables with respect to which you compute the vector potential.

More About

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