Electromagnetic

Coulomb’s law:

there is force between each two charge $F = K_e\frac{q_1q_2}{d^2}$, ($K_e$ is coulomb’s constant: $8.988\times10^9 Nm^2/C^2$).
then any charge create a field that can effect any other charge in his space so we call this field as Electric Field. Electric field over a sphere with a charge inside $E = \frac{F}{q_t} = \frac{q}{4\pi\varepsilon_oR^2} (N/C) (K_e = \frac{1}{4\pi\varepsilon_o})$

Electric flux:

$\phi_E = \oint\overline{E}.\overline{dA}$

where E ($\frac{N}{C}$ $\frac{newton}{colomb}$) is Electric field and A ($m^2$) is orthogonal tiny surface so $\phi_E$ unit is ${Nm^2}/C$

Quass’s law

over a closed surface: $\phi_E = \frac{q_{Total}}{4\pi\varepsilon_oR^2} * 4\pi R^2 = \frac{q_{Total}}{\varepsilon_o}$

where q is total charge inside the closed surface and The constant $\varepsilon_o$ is *vacuum electric permittivity*.

Ampere’s law

$\oint\overline{B}.\overline{dl} = {\mu}I$

Faraday’s law

changing magnetic flux => EMF (Electromotive Force) $\varepsilon_{EMF} = -\frac{d\phi_M}{dt}$ where magnetic flux is $\phi_M = \oint B \cdot dA$

\[\varepsilon_{EMF} = \frac{W}{q} = \frac{\oint F.dl}{q} = \oint E.dl\] \[\boxed{\oint\overline{E}.\overline{dl} = -\frac{d\phi_M}{dt}}\]