Scalar potential (Question 2 (15+5=20 Marks)) — UPSC Physics Optional IFoS 2018 Paper I

Using the set of four Maxwell's equations, obtain the Lorentz condition relation between the scalar potential \phi and vector potential A, i.e., \nabla \cdot A + \frac{1}{c^2} \frac{\partial \phi}{\partial t} = 0 and discuss the gauge transformations, Lorentz gauge and Coulomb gauge.