Question

Two half-wave dipole antennas placed as shown in the figure are excited with sinusoidally varying currents of frequency 3 MHz and phase shift of $\pi /2$ between them (the element at the origin leads in phase). If the maximum radiated E-field at the point P in the x-y plane occurs at an azimuthal angle of ${60}^{\circ }$, the distance d (in metres) between the antennas is

• A. 50

Answer 1

The correct option is A 50
Both dipole antennas have isotropic pattern in $\varphi$ view or H plane view.

$\Psi =\beta dcos\theta +\alpha$

where, $\alpha =-{90}^{\circ },\beta =\frac{2\pi }{\lambda }=\frac{2\pi }{\frac{3\times {10}^8}{3\times {10}^6}}=\frac{2\pi }{100}$

Since maximum radiation $(\Psi =0)$ is at $\theta ={60}^{\circ }$

$\Rightarrow 0=\frac{2\pi }{100}dcos{60}^{\circ }-{90}^{\circ }$

$\Rightarrow 90=\frac{360}{100}d\frac{1}{2}$

$\Rightarrow d=50m$