# Maxwell’s Equations

Our physics 54 class has now been introduced to all four of Maxwell’s equations. We do not have Maxwell’s correction to Ampere’s Law yet, but man we are close. Our current version of these really beautiful equations:
Gauss’s Law for Electricity
$\oint_S \vec{E} \cdot \hat{n} dA = \frac{1}{\epsilon_o}\int_{V/S} \rho_e dV$

Gauss’s Law for Magnetism[experimentally — no magnetic monopoles]
$\oint_S \vec{B} \cdot \hat{n} dA = {\mu_o}\int_{V/S} \rho_m dV = 0$

Ampere’s Law [not yet fixed]
$\oint_C \vec{B} \cdot d\vec{l} = {\mu_o}\int_{S/C} \vec{J}_e \cdot \hat{n} dA = \mu_o I_{thru C}$

$\oint_C \vec{E} \cdot d\vec{l} = - \frac{d}{dt}\int_{S/C} \vec{B} \cdot \hat{n} dA$