$$ \text{Cartesian to spherical coordinates: }\begin{align*} R &= \sqrt{x^2 + y^2 + z^2} \\\theta &= \tan^{-1}\left(\frac{\sqrt{x^2 + y^2}}{z}\right) \\\phi &= \tan^{-1}\left(\frac{y}{x}\right)\end{align*} \newline dV = r^2 \sin(\theta) \, dr \, d\theta \, d\phi
$$
$$ \text{Cartesian to cylindrical coordinates: } \begin{align*} r &= \sqrt{x^2 + y^2} \\ \phi &= \tan^{-1}\left(\frac{y}{x}\right) \\ z &= z \end{align*}
$$
$$ \text{Normal component: } \vec E_n = (\vec E \cdot \hat r) \hat r \newline \text{where } \hat r \text{ points radially outwards} \newline \newline \text{Tangential component: } \vec E_t= \vec E - \vec E_n $$
Coulomb’s law is valid charges are:
What about line, surface, and volume charges?
At atomic scale, charge distribution is discrete
$P_v = \lim _{\triangle Q → 0} \frac{\triangle q}{\triangle v} = \frac{dq}{dv}$
