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## a question on flux, and on field integration

hey all,
i've recently started studying electrostatics, and i have couple of question about things that i did not fully understand, and would very much appreciate if someone could set me straight.

1) how can a cube, with a single charge in the middle of it have a flux? don't the field lines cancel each other, thus achieving 0 electric field for each plane? i mean, you have a field vector going up on the Y axis, and down on the same axis (and so on for the others), so how come the flux $\Phi=A\overline{E}$ isn't zero?

2) if i have a flat disk on a plane, with uniform charge density $\sigma$, why when i integrate, i do so for small rings, and not for very small circles? why is it: $E=\int\frac{kσ2∏rdr}{(...)}$ instead of $E=\int\frac{kσ2∏dr}{(...)}$?

thank you very much for your help
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