The magnetic field of an electromagnetic (em) plane wave in free space is represented by bb�⃗(zz, tt) = bb0(xx� + (ii/2)yy�)eeii(−ωωωω) where ii = √−1. (a) in what direction is the em wave propagating? what is its propagation speed and its wavelength λλ in terms of the constants given above? [2pts] (b) sketch (the real part of) bb�⃗ in the xy plane at kz = π/2 at quarter-period intervals, at the times t = 0, t/4, t/2 and 3t/4 (where t is the period of the wave). this wave is called an elliptically polarized wave, why? [1pt] (c) calculate the corresponding electric field ee�⃗ and sketch it at the four times specified in part (b). [1pt] (d) find the poynting vector ss⃗ and calculate the power density s carried by the wave. [1pt] (e) the em wave passes through a thin plate of special material which delays the x- component of the magnetic field bx by a phase π/2, so that bx is represented by bb0eeii(−ωωωω+ππ/2) . the y-component of the magnetic field in unaffected. calculate ee�⃗ and sketch ee�⃗ and bb�⃗ at quarter-period intervals, as in parts (b) and (c). [1pt]