Coulombs law

Electric Field

\(\vec{E} = \dfrac{\vec{F_0}}{q_0}\\\) Where:
$\vec{E}$ is the electric field
$\vec{F_0}$ is the force experienced at a point in the electric field
$q_0$ is the Test charge

Electric Field of a Point Charge

\(F(x,y,z) = \dfrac{1}{4\pi\epsilon_0} \dfrac{q_1q_0}{r^2}\\ E(x,y,z) = 1\dfrac{F(x,y,z)}{q_0}\\ E_p(x,y,z) = \dfrac{1}{4\pi\epsilon_0} \dfrac{q_1}{r^2} u \\\) The electric field is measure in Newton/Coulomb

Superposition of Electric Fields generated by point charges

\[F= \sum_{i} F_i\]

Eletric field computation: continuous distribution of charge

Line Charges

$dE = \dfrac{1}{4\pi\epsilon_0}\dfrac{q_i}{r^2_i}$

Disk charges

Cube charges

\[E = \int\dfrac{1}{4\pi\epsilon_0}\dfrac{dq}{r^2}u\]

Charge density

Linear charge density

\[\lambda = \dfrac{q}{\mathscr{l}}\]

A linear charge where \(y \gg l\) then it practically becomes a point charge
A linear charge where \(y \ll l\) then it is…

Surface charge density

\[\sigma = \dfrac{q}{\mathscr{l}^2}\]

check what happens when the surface of the disk tends to $\infty$

Volume charge density

\[\rho = \dfrac{q}{\mathscr{l}^3}\]