(1)In dielectric and magnetic material, unusual situations arise when the electric permittivity and magnetic permeability are both real and negative….

(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 – ωt)] and magnetic field H = H0 exp[-i(k.r – ωt)].(a) First consider a standard material with permittivity ε and magneticpermeability μ 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 ε = – | ε | and μ = – |μ| 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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