a really hard one here. would appreciate if you could start me off:

a physical system is governed by the following:

curlE= $\displaystyle -\frac{\partial B}{\partial t}$,

divB= 0,

curlB = J+ $\displaystyle \frac{\partial E}{\partial t}$,

divE =$\displaystyle \rho$

where t = time, and time derivatives commute with $\displaystyle \nabla$

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how could you show that $\displaystyle \frac{\partial p}{\partial t}$ + divJ = 0when $\displaystyle \rho = 0$ and

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J =0 everywhere how can you show that:

$\displaystyle \nabla^2E - \frac{\partial^2E}{\partial t^2}$ = 0

and

$\displaystyle \nabla^2B - \frac{\partial^2B}{\partial t^2}$ = 0