A uniform plane electromagnetic wave traveling in free-space enters into a lossless medium at normal incidence. In the medium its velocity reduces by 50% and in free space sets up a standing wave having a reflection coefficient of - 0.125. Calculate the permeability and the permittivity of the medium.

A 300 MHz plane E.M. wave is propagating in free space. The wave is incident normally on an infinite copper slab. For the transmitted wave in the copper slab, calculate the following

(a) Attenuation constant
(b) Phase constant
(c) Skin depth
(d) Phase velocity and
(e) Group velocity

for copper assume the following values
Conductivity $$\sigma = 5.8 \times {10^7}$$ $$mho/m$$
Permeability $$\mu = 4\pi \times {10^{ - 7}}$$ $$H/m$$
Permeability $$\varepsilon = {1 \over {36\pi }} \times {10^{ - 9}}$$ $$F/m$$

An electric field is given by $$\overrightarrow E = \overrightarrow a {}_x\,{\rm A}\,\,\sin \,\beta ySin\,\,\omega t$$ is present in a charge free medium infinite in extent

(a) Determine the associated magnetic field.
(b) What type of wave does the above field represent?