Using Maxwell’s equations in free space, derive the wave equation for the y-component of the electric field vector.

To derive the wave equation for the y-component of the electric field vector (\(E_y\)) using Maxwell's equations in free space, we can start with the differential form of Maxwell's equations. In free space, these equations are given by:

1. Gauss's Law for Electric Fields:
   \[ \nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0} \]

2. Gauss's Law for Magnetic Fields:
   \[ \nabla \cdot \mathbf{B} = 0 \]

3. Faraday's Law of Electromagnetic Induction:
   \[ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} \]

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