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Suppose we have a sphere, with a radius a and a total charge $Q_{0}$, immersed in a conductor, with a conductivity $\sigma$ and a permittivity $\epsilon$ .The sphere releases a current density: $$ j= \sigma E$$ So, utilizing Maxwell's first law for an imaginary sphere of radius r, we can find the electric field: $$E = \frac{Q(t)}{4\pi\epsilon r^2} $$ And so the differential equation: $$ \frac{dQ(t)}{dt} = -\frac{\sigma}{\epsilon}Q(t)$$ This, though, only takes into consideration the current charge of the sphere of radius a, without considering the charge inside the radius r caused by j flowing inside. Why doesn't the density current influence the electric field even if it is inside the radius r? Is it simply neglected because small in comparison to the total electric field?

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The fact that there's a current in a material doesn't imply there must be a charge imbalance in that material.

For example, in a copper wire, even when there are mobile electrons carrying a current, there are also protons with positive charge present. They don't contribute to current because they are not mobile, but fixed in place.

It is possible to produce a charge imbalance in a conductctive material (for example on a plate of a capacitor) but the mere fact of current present doesn't tell you that there is one.

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