Answer Happy

3. (a) Time-dependent electric field E(7,t) and magnetic field B (7,t) can also be obtained from a set of potentials; a scalar electric potential V(7, t) and a vector magnetic field A(7,t) in a medium. i) Write the expressions for the fields in terms of the two potentials. ii) Is the chosen pair of potentials unique? Explain your answer. (b) From the potential pair one can also find the charge-current source that generates the fields. The potentials in a region of empty space are described by the following equations; V(x,y,z,t) = 0, A(z,y,z,t)= 4c ō, -(ct-|x|)³k, for <ct for z>ct where the constant k = 26.5 A/sm, c is the speed of light and t is time in ns. i) Determine the electric and magnetic field from the potentials. ii) Determine the charge-current source that generates these fields. iii) Discuss the situation where z> et. (c) i) Write and explain briefly the Jefimenko's equations. ii) Describe briefly the extra information needed about the charge-current source before you can apply the Jefimenko's equations. iii) Which gauge transformation would be satisfied by the solutions of Jefimenko's equations?