Question

2.(a). By considering a circuit containing a capacitor shown below, explain briefly why Ampere's law B.dr Ho,1(S,) needs to be modified to allow for time-varying fields. What modification is needed to correct the equation? [3] -Q I s, is a surface bounded by the curve C and cutting the wire. (b). The magnetic field in free space due to a monochromatic plane wave is of the form: B(x, y,z,t) B, cos(kz-ax) where Bo, k and ware constants. Write down the dispersion relation for this wave. [2] (i). Calculate the curl of the B field using the determinant, (ii. x- VxB [3] ax ay Oz B B By State the Ampere-Maxwell law in differential form in vacuum. [2] (iii). (iv). Use the results in (ii) and (iii) to derive an expression for the electric field E(x, y, z, t) in the wave in the vacuum. [5] (v). Explain how the properties of a monochromatic plane wave reflecting normally off a plane interface can be used to determine the frequency of the wave. [5]

Answer 1

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