Problem $2$ A research team in UQ would like to use electromagnetic wave $($EM$)$ as a non contact optical probe to study matter properties. The leading principal investigator decides to demonstrate the utility of EM waves on two materials, sea water and graphite, by collaborating with environmental scientists and chemical engineers. a$)$ Sea water: A linearly polarised uniform plane wave propagating in the $+$ direction in sea water $(=80,=1,=4$ S$/$m$),$ the magnitude of the field intensity is: $0\mathrm{.}1(10/3)$ A$/$m$,$ at $=0.1)$ Determine the attenuation constant, the phase constant, the intrinsic impedance, the phase velocity, the wavelength, and the skin depth. $2)$ Find the location at which the amplitude of $$ is $0\mathrm{.}01$ A$/$m$.3)$ Write the expression for $(,)$ and $(,)$ at $=0\mathrm{.}5$ m as functions of $.$ b$)$ Graphite: Given that the skin depth for graphite at $100$ MHz is $0\mathrm{.}16$ mm$,$ determine: $1)$ The conductivity of graphite, $2)$ The distance that a $1$ GHz wave travels in graphite such that its field intensity is reduced by $30$ dB$.$