Monthly Archives: July 2024

Problem: Write down the current density \(\mathbf J(\mathbf x,t)\) of an idealized Hertzian dipole. Hence, calculate the electric and magnetic fields \(\mathbf E(\mathbf x,t),\mathbf B(\mathbf x,t)\) of the Hertzian dipole. Solution: The current density for a Hertzian electric dipole \(\boldsymbol{\pi}(t)\) … Continue reading →

Problem: Let \(\psi(\mathbf x),\phi(\mathbf x)\) be arbitrary complex-valued maps on \(\mathbf x\in\mathbf R^d\) (in practice this could also just be time domain signals \(\psi(t),\phi(t)\), etc.). Define their convolution \((\psi*\phi)(\mathbf x)\) and their cross-correlation \((\psi\star\phi)(\mathbf x)\), and state how they are … Continue reading →

The goal of physics is to understand the what, how, and why of the universe. The twist is that sometimes one sometimes has to introduce auxiliary physical quantities as stepping stones towards such an understanding. An exemplar of this in … Continue reading →