Question

The induction and radiation fields are equal at a distance of _______

(a) λ/4

(b) λ/6

(c) λ/8

(d) λ/2

The question was asked in an international level competition.

I'm obligated to ask this question of Basics in chapter Antenna Parameters of Antennas

Answer 1

Right answer is (b) λ/6

The explanation is: For an Hertzian dipole, equating the magnitudes of maximum induction and radiation fields we get,

\(\mid \overline{E_θ}\mid_{max⁡Radiation} =\mid \overline{E_θ}\mid_{max⁡Induction} \)

\(\frac{I_m dl}{4\pi\epsilon} (\frac{ω}{v^2r})=\frac{I_mdl}{4\pi\epsilon} (\frac{1}{r^2v})\)

\(r=\frac{v}{ω}=\frac{\lambda f}{2\pi f}=\frac{\lambda}{6}.\)