(adsbygoogle = window.adsbygoogle || []).push({}); Biot-Savart + Coulomb + Charge Conservation = Maxwell??

Do the Biot-Savart Law, Coulomb's Law, and the Law of Charge Conservation contain the same information as Maxwell's Equations? i.e.

[tex]

\begin{cases}

d\vec{B} = \frac{\mu_o}{4\pi} \frac{I d\vec{l} \times \hat r }{r^2} \\

\vec{E}= \frac{1}{4\pi\varepsilon_o} \frac{Q \hat r}{r^2} \\

\nabla \cdot \vec{J} = -\frac{\partial \rho}{\partial t} ,

\end{cases}

\overset{?}{=}

\begin{cases}

\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0} \\

\nabla \cdot \vec{B} = 0 \\

\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t} \\

\nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t},

\end{cases}

[/tex]

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# Biot-Savart + Coulomb + Charge Conservation = Maxwell?

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