We first write out Maxwell’s equations in differential form, as we have already shown for Gauss’ Law (Section 17.4) and ’s Law (Section 22.3) \[\begin{aligned} \nabla \cdot \vec E &= \frac{\rho}{\epsi...We first write out Maxwell’s equations in differential form, as we have already shown for Gauss’ Law (Section 17.4) and ’s Law (Section 22.3) \[\begin{aligned} \nabla \cdot \vec E &= \frac{\rho}{\epsilon_0} &\text{(Gauss' Law)}\\ \nabla \cdot \vec B&= 0 &\text{(No magnetic monopoles)}\\ \nabla \times \vec B &= \mu_0 \left(\vec j + \epsilon_0\frac{\partial \vec E}{\partial t}\right) &\text{(Ampere's Law)}\\ \nabla \times \vec E &= -\frac{\partial\vec B}{\partial t} &\text{(Faraday's Law)}\\\end{…