(1)In dielectric and magnetic material, unusual situations arise when the electricpermittivity and magnetic permeability are both real and negative. Consider a plane wave with electric field E = E0 exp[-i(k.r – ?t)] and magnetic field H = H0 exp[-i(k.r – ?t)].(a) First consider a standard material with permittivity ? and magneticpermeability ? both real and positive. Find the Maxwell equations satisfied by E0 and H0 in such a medium, the velocity of light in such amedium, and what combination of E0, k and H0 form a right-handed set.(b) From now on we consider a doubly-negative meta-material and write ? = – | ? | and ? = – |?| Write the Maxwell equations satis_ed by E0and H0 in the meta-material and show that the role of E0 and H0 areinterchanged compared to the standard case explored in (1). (c) What can you state about the set (E0;H0; k)?
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