Interactions between light and matter
- Page ID
- 62523
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Maxwell's Electrodynamics Equations:
\begin{eqnarray}
1. \nabla\cdot E &=& \frac{\rho}{\epsilon_0}\\
2. \nabla\cdot B &=& 0\\
3. \nabla\times E &=& -\frac{\partial B}{\partial t}\\
4. \nabla\times H &=& \mu_0\left(\frac{\partial D}{\partial t}+J\right)
\end{eqnarray}
Consider the simple eq. 2, we can say that \[B = \nabla\times A\] as gradient of a curl of a vector is zero. This also implies the existence a vector field (A), however, we need to realize the nature of that field.
Using this in eq. 3, we get \[\nabla\times \left( E+\frac{\partial}{\partial t} A\right) = 0\]
So, E+\frac{\partial}{\partial t} A