Maxwell's equations relating the electric field 𝐄 and magnetic field 𝐇 as they vary with time in

(a) We know that $nabla times(nabla times mathbf{E})=nabla(nabla cdot mathbf{E})-nabla^{2}mathbf

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Maxwell's equations relating the electric field $\mathbf{E}$ and magnetic field $\mathbf{H}$ as they vary with time in a region containing no charge and no current can be stated as follows: $\operatorname{div} \mathbf{E}=0 \quad$ div $\mathbf{H}=0$ $\operatorname{curl} \mathbf{E}=-\frac{1}{c} \frac{\partial \mathbf{H}}{\partial t}$ $\mathrm{H} \mathrm{H}=\frac{1}{c} \frac{\partial \mathrm{E}}{\partial t}$ where $c$ is the speed of light. Use these equations to prove the following: (a) $\nabla \times(\nabla \times \mathbf{E})=-\frac{1}{c^{2}} \frac{\partial^{2} \mathbf{E}}{\partial t^{2}}$ (b) $\nabla \times(\nabla \times \mathbf{H})=-\frac{1}{c^{2}} \frac{\partial^{2} \mathbf{H}}{\partial t^{2}}$ (c) $\nabla^{2} E=\frac{1}{c^{2}} \frac{\partial^{2} E}{\partial t^{2}}$ IHint: Use Exercise 29.1 (d) $\nabla^{2} \mathbf{H}=\frac{1}{c^{2}} \frac{\partial^{2} \mathbf{H}}{\partial t^{2}}$

          Maxwell's equations relating the electric field $\mathbf{E}$ and magnetic field $\mathbf{H}$ as they vary with time in a region containing no charge and no current can be stated as follows:
$\operatorname{div} \mathbf{E}=0 \quad$ div $\mathbf{H}=0$
$\operatorname{curl} \mathbf{E}=-\frac{1}{c} \frac{\partial \mathbf{H}}{\partial t}$
$\mathrm{H} \mathrm{H}=\frac{1}{c} \frac{\partial \mathrm{E}}{\partial t}$
where $c$ is the speed of light. Use these equations to prove the following:
(a) $\nabla \times(\nabla \times \mathbf{E})=-\frac{1}{c^{2}} \frac{\partial^{2} \mathbf{E}}{\partial t^{2}}$
(b) $\nabla \times(\nabla \times \mathbf{H})=-\frac{1}{c^{2}} \frac{\partial^{2} \mathbf{H}}{\partial t^{2}}$
(c) $\nabla^{2} E=\frac{1}{c^{2}} \frac{\partial^{2} E}{\partial t^{2}}$ IHint: Use Exercise 29.1
(d) $\nabla^{2} \mathbf{H}=\frac{1}{c^{2}} \frac{\partial^{2} \mathbf{H}}{\partial t^{2}}$

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