We know that the Gauss's law expressed in the differential form is:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\mathbf{\nabla}\cdot\mathbf{E} = \frac{\rho}{\epsilon_0}[/tex],

right?

I read at wikipedia that [tex]\rho[/tex] is: the total charge density including dipole charges bound in a material.

I don't understand...

The left side of equation is the divergence of the field vector E (electric field), right?

The divergence is the measure of the flux density at a given point in space (so it's a function of x,y,z considering 3D), right?

So the flux density at any point in the electric field will be different (unless we have uniform field), because in some regions the field lines are more (convergent? next, near, you got it) and in other regions the field lines are more separate, right?

The the right side of the equation is a constant. It is the total charge density divided by the permittivity... So this is telling me that the flux density is the same for ALL points in the space, isn't it?

Or is the density on the right side the density of the point I'm calculating he divergence?

Where am I wrong?

I appreciate the help,

Thank you

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# Doubt about differential Gauss's law

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