(a)The Ampere’s circuital law as it applies to steady magnetic fields (∇ x E = J) shows its inadequacy for time-varying conditions. Prove its inadequacy for time-varying conditions using the equation of continuity (∇.J = − ∂ρv ∂t ) and derive complete expression of Ampere’s circuital law for time varying fields.

 (b) Let µ = 4x10−5H/m,  = 2x1010F/m, and δ = 0 everywhere. If H = 8 cos(1010t − βx) az A/m, use Maxwells equations to obtain expressions for B, D, E, and β.