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By the way i am Not interesting strictly to the elettric field but is more how to calculate it. the surface integral is Not possibile because of the normal vector, the gauss Theorem neither, i do Not see a simmetry to get the electric field out from the integral
maybe you did not understand my questions which is: how can I see that if does not exist heat engine which works with only two sources that has efficiency more of the Carnot' s one, than •does not exist _any heat machine with efficiency equal to 1 Or •we can't make a transform having as unique effect to transfer heat form a cold body to an hot body Or •we can't transfor with a cycle all heat absorbed into work Or •deltaS>=0 Hope this time the question is more clear