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Homework #12: Do not turn these in since there is a test next week (Friday, April 25).
 Here is a vector with its x, y and zcomponents: A={x^{3}z, y^{2}sin(kx), z^3}. Calculate (a) ∇(∇⋅A), and (b) ()∇^{2}A. Show all of your stepsno shortcuts.
 Here is a set of Maxwelllike equations:
∇xK=a(∂L/∂t)
∇xL= b(∂K/∂t)
∇⋅K=0
∇⋅L=0
(a) Derive the wave equation for K.
(b) Derive the wave equation for L.
(c) Find the wave speed for these fields in terms of the constants 'a' and 'b.'
 (a) Evaluate e^{iπ/8} in terms of its real an imaginary ports. (b) Write i^{1/6} using an exponential.
 Here is an electric field traveling in free space: E=zE_{0}e^{i(ky+ωt)} where z is the unit vector in the zdirection.
 Draw this electric field as it travels.
 Find the magnetic field B associated with this electric field.
 The frequency of this wave is f=100MHz. Find the wavenumber 'k' associated with this wave.
 Here is a magnetic field traveling in free space: B=xB_{0}e^{i(kz+ωt)} where x is the unit vector in the x direction.
 Draw this magnetic field as it travels.
 Find the electric field E associated with this magnetic field.
That's all for homework #12.
