Write down Maxwell's field equations for free space and obtain expressions for velocity of electromagnetic waves.

Maxwell's equations in free space describe how electric and magnetic fields propagate and interact with matter. In the absence of free charges and currents, the equations simplify. The four Maxwell's equations in free space are:

1. Gauss's law for electricity:  
   \(\nabla \cdot \mathbf{E} = 0\)  
   This implies that there are no electric charges in free space, meaning the electric field is solenoidal (divergence-free).

2. Gauss's law for magnetism:  
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