Question

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

Answer 1

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

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

\(\frac{dϵ_r}{dH}=2n \frac{dn}{dH}\)