3 (a) ii) A time-dependent electric field in vacuum is given by ⃗E= E0(0, 0, sin(ky − ωt)) where E0 is a constant. Derive an expression for the corresponding magnetic field ⃗B.  Using curl E=-dB/dt I end up with B=(E0/c)sin(ky-wt) Show that both ⃗E and ⃗B are perpendicular to the wave vector ⃗k = (0, k, 0).  Using the dot product i found that: k.E=(0x0,0xk,0x ⃗E)=0 k.B=(0x ⃗E/c,0xk,0x0)=0 What is the Poynting vector for this wave?  N=(ExB)/μ0μr Then we get: (1/μ0μr)((E0 2/c)sin(ky-wt)2,0,0) Finally giving: (-1/μ0.μr.c)(E02Sin(ky-wt)2) I think the first two parts are right but have no idea if im doing the right thing on the last part. I have used the cross product between E and B and got my final answer for part 3. Thanks for any help in advance!