OB V X E = atLet E = &Ex(z, t) where Ex(z, t) = Eo cos(wt F Bz + 4) and Eo (amplitude), w (angular fre- quency), B (wavenumber), and o (phase shift) are positive real scalars. These fields describe wave polarized in the x direction and propagating in the +2 direction, respectively. a) Show that the specified Ex satisfies the wave equation derived above if: B = WVHOCO = where c ~ 3 x 10'm/s is the speed of light in free space. b) Substitute the specified Ex into Faraday's law and solve for B(z, t) assuming that B(0, 0) = F Ex (0,0) C y. Show that your answer can be expressed as B = 1-ry (be careful about maintaining the correct order for the upper and lower signs). Are there any restrictions on the value for ?