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quasar987

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In the real world, on a small enough scale, linear charge distribution and surface charge distributions do not exist. It all comes down to [itex]\rho[/itex]. Same for the currents; there are only current densities [itex]\vec{J}[/itex]. So in lights of this, it is satifying to say that the Maxwell's equations are

[tex]\nabla \cdot E = \rho/\epsilon_0[/tex]

and

[tex]\nabla \times B = \mu_0 J + \mu_0 \epsilon_0 \partial E/ \partial t[/tex]

But in textbook exercices, as well as in real life approximations, we DO deal with linear and surface densities and currents. So in lights of this, aren't these two equations written in a more GENERAL form in their integral apearance:

[tex]\epsilon_0 \oint E \cdot da = Q_{enc}[/tex]

and

[tex]\oint B \cdot dl = \mu_0 I_{enc} + \mu_0 \epsilon_0 \int \frac{\partial E}{\partial t} \cdot da[/tex]

???