Poisson's Differential Equation for Rotational and Solenoidal Field/Examples/Magnetic Field in Conductor carrying Steady Current

Example of Poisson's Differential Equation for Rotational and Solenoidal Field
Consider a conductor of electricity $C$.

Let $C$ be carrying a steady current $I$.

From Curl Operator: Magnetic Field of Conductor, the curl of the magneto-motive force per unit area $\mathbf H$ is given by:

We have from Ampère's Law that:
 * $\curl \mathbf H = \mathbf J$

Hence this satisfies Poisson's Differential Equation for Rotational and Solenoidal Field:
 * $\curl \mathbf J = -\nabla^2 \mathbf J$