Einstein’s Field Equations $$ \begin{equation} G_{\mu \nu} + \Lambda g_{\mu \nu} = 8\pi T_{\mu \nu} \end{equation} $$This innocent looking equation packs one of the most startling concepts of all of nature. This is a stub article, I will update it gradually.
Classical Electrodynamics In the early days of the encounter with Electricity and magnetism, these were studied seperately as independent phenomenon in nature. With more studies, it was evident that Electricity and magnetism were intimately related. Maxwell painstakingly combined the known laws of electricity and magnetism into a set of four beautiful first order differential equations and showed the intimate connection. $$ \begin{align*} \nabla \cdot \vec{B} &= 0 \end{align*} $$$$ \begin{align*} \nabla \cdot \vec{E} &= \frac{\rho}{\epsilon_0} \end{align*} $$$$ \begin{align*} \nabla \times \vec{E} - \frac{\partial \vec{B}}{ \partial t} &= 0 \end{align*} $$$$ \begin{align*} \nabla \times \vec{B} - \frac{\partial \vec{E}}{\partial t} &= \vec{J} \end{align*} $$$$ \begin{align*} \vec{F} = q(\vec{v}\times \vec{B} + \vec{E}) \end{align*} $$In classical electrodynamics the four maxwells’ equation together with the Lorentz force law form the complete set of equation required to understand all electromagnetic phenomenon. ...