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Relation between gradient of refractive index with height and dielectric constant gradient is ____________(a) \(\frac{dϵ_r}{dH}=2n \frac{dn}{dH}\)(b) \(\frac{dϵ_r}{dH}=n \frac{dn}{dH}\)(c) \(\frac{dϵ_r}{dH}=2n/\frac{dn}{dH}\)(d) \(\frac{dϵ_r}{dH}=-2n \frac{dn}{dH}\)This question was addressed to me during an online exam.Query is from Space Wave Propagation topic in chapter Space Wave Propagation of Antennas

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The CORRECT choice is (a) \(\frac{dϵ_r}{dH}=2n \frac{dn}{dH}\)

EXPLANATION: REFRACTIVE index is \(n=n=\sqrt{ϵ_r μ}= n=\sqrt{ϵ_r} (μ=1)\)

DIFFERENTIATING with respective heights treating n, ϵ_r as dependent variables

\(\frac{dn}{dH}=\frac{1}{2} \frac{1}{\sqrt{ϵ_r}} \frac{dϵ_r}{dH}\)

\(\frac{dϵ_r}{dH}=2n \frac{dn}{dH}\)



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