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In classical electrodynamics, the behavior of electromagnetic fields in vacuum is governed by Maxwell's equations. In free space, where there are no charges or currents, these equations reduce to: [ \nabla \cdot \mathbf{E} = 0, \quad \nabla \cdot \mathbf{B} = 0, ] [ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}, \quad \nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}. ] To derive the electromagnetic wave equation for the electric field (\mathbf{E}), we take the curl of Faraday’s law: [ ____ ________ __________ __________ ___ _______ ________ ______ _________ _________.
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