Electromagnetism, also known as Electricity & Magnetism or E&M, is one of the fundamental forces of nature. It can be described by the beautiful Maxwell’s Equations:

\[\begin{align} \nabla \cdot \mathbf{E} &= 4 \pi \rho_e \\\\ \nabla\cdot \mathbf{B} &= 0 \\\\ \nabla\times\mathbf{E} &= -\frac{1}{c}\frac{\partial\mathbf{B}}{\partial t} \\\\ \nabla\times\mathbf{B} &= \frac{1}{c}\frac{\partial\mathbf{E}}{\partial t} + \frac{4 \pi}{c}\mathbf{J}_e \end{align}\]

Though seemingly simple, these equations have profound consequences, especially in the presence of materials (which require a slightly more sophisticated formulation).

  • The Physics of Maxwell's Equations
    [Mathematical Physics] Maxwell’s Equations govern the study of electromagnetism, one of the fundamental forces of nature. Here, I attempt to motivate these beautiful equations and present some of their more interesting consequences.