Q$\mathrm{.}1.25\%$ A plane wave traveling in a certain material $(={}_r{}_0,={}_0)$ has the electric field intensity phasor given by

tilde$(E)(y,z)=12(10a_x+8a_y-6a_z)e^{-j1z(3y+4z)}\frac{V}{m}$

It is known that the phase velocity in this medium is $\frac{c}{3},c$ being the speed of light in free$-$space.

a$)5\%$ Find the relative permittivity $({}_r)$ of this material.

b$)2\mathrm{.}5\%$ What is the propagation constant $(k)$ of the wave?

c$)2\mathrm{.}5\%$ Give the unit vector $(a_n)$ in the direction of propagation of this wave.

d$)2\mathrm{.}5\%$ Find the wavelength $(2).$

c$)2\mathrm{.}5\%$ Determine the frequency $(f)$ of the wave.

f$)7\mathrm{.}5\%$ Find the associated magnetic field phasor $($H$).$

g$)2\mathrm{.}5\%$ Give the time domain expression, $,$ for the magnetic field.