Poisson's Differential Equation for Rotational and Solenoidal Field/Examples/Magnetic Field in Conductor carrying Steady Current
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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:
- $\curl \mathbf H = \mathbf J$
Hence this satisfies Poisson's Differential Equation for Rotational and Solenoidal Field:
- $\curl \mathbf J = -\nabla^2 \mathbf J$
Sources
- 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {V}$: Further Applications of the Operator $\nabla$: $7$. The Classification of Vector Fields: $\text {(iii)}$