[UPSC IFoS 2014] Electromagnetic Theory (Q360, 5+5+10=20M)

(i) Write Maxwell's equations in the absence of a medium. (ii) Explain the gauge transformation and gauge invariance. Show that the relation \text{div } \bar{A} + \frac{1}{c} \frac{\partial \phi}{\partial t} is Lorentz-covariant, where \bar{A} and \phi are the vector potential and the scalar potential respectively. (iii) Obtain Maxwell's wave equations satisfied by the scalar and vector potentials in the absence of charge and current.