Energy inequality in the time domain

Now we integrate both sides of equation (8.98) over a time period  

Taking into account that all integrals on the right-hand side of expression (8.99) are non-negative, we arrive at the important energy inequality, 

Formula (8.100) has a clear physical interpretation the total energy radiated out of the domain with sources of electromagnetic field, over the time period from the initial field generation until any time t, is always non-negative. Thus, the electromagnetic sources continuously radiate energy outside these. sources  

The last inequality means that the energy introduced through the extraneous currents y always exceeds the sum of the energy dissipated in Joule heat within the domain V1 and the electric and magnetic energy stored in the volume Vi. In other words, there is always a net radiation of electromagnetic energy from any source. 

An obvious result follows immediately from this equation, namely that in this case the electromagnetic field is equal to zero as well  

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