If a vector field $\vec V$is related to another vector field $\vec A$through $\vec V$= $\nabla$x $\vec A$, which of the following is true? (Note : C and S_c refer to any closed contour and any surface whose boundary is C.)

A $\dfrac{\lambda}{2}$ dipole is kept horizontally at a height of $\dfrac{\lambda_0}{2}$ above a perfectly conducting infinite ground plane. The radiation pattern in the plane of the dipole ($\vec E$ plane) looks approximately as

Characteristic impedance of a transmission line is 50$\Omega$. Input impedance of the open circuited line is Z_oc = 100 + j150$\Omega$. When the transmission line is short-circuited, the value of the input impedance will be

A plane wave having the electric field component $E_1$ = 24 cos(3$\times$10⁸t -$\beta$y)$\widehat a_z$V/m and traveling in free space is incident normally on a lossless medium with m = m₀ and e = 9e0 which occupies the region y ≥ 0. The reflected magnetic field component is given by

A plane electromagnetic wave propagating in free space is incident normally on a large slab of loss-less, non-magnetic, dielectric material with $\epsilon \gt \epsilon_0$. Maxima and minima are observed when the electric field is measured in front of the slab. The maximum electric field is found to be 5 times the minimum field. The intrinsic impedance of the medium should be

A rectangular metal wave-guide filled with a dielectric material of relative permittivity $\epsilon_r$ = 4 has the inside dimensions 3.0 cm $\times$ 1.2 cm. The cut-off frequency for the dominant mode is

In the circuit shown, all the transmission line sections are lossless. The Voltage Standing Wave Ration (VSWR) on the 60W line is

The direction of vector A is radially outward from the origin, with |A| = k rⁿ where r² = x² + y² + z² and k is constant. The value of n for $\nabla$. A = 0 is

A mast antenna consisting of a 50 metre long vertical conductor operates over a perfectly conducting ground plane. It is base-fed at a frequency of 600 kHz. The radiation resistance of the antenna in Ohms is

A right circularly polarised (RCP) plane wave is incident at an angle of 60° to the normal, on an air-dielectric interface. If the reflected wave is linearly polarised, the relative dielectric constant ^{$\epsilon_{r2}$} is

A lossless transmission line is terminated in a load which reflects a part of the incident power. The measured VSWR is 2. The percentage of the power that is reflected back is

Voltage standing wave pattern in a lossless transmission line with characteristic impedance 50 $\Omega$ and a resistive load is shown in figure.

The reflection coefficient is given by

Voltage standing wave pattern in a lossless transmission line with characteristic impedance 50 $\Omega$ and a resistive load is shown in figure.

The value of the load resistance is

A medium is divided into regions I and II about x = 0 plane, as shown in the figure below. An electromagnetic wave with electric field E₁ = 4$\widehat a$_x + 3$\widehat a$_y + 5$\widehat a$_z is incident normally on the interface form region-I. The electric field E₂ in region-II at the interface is

Two identical antennas are placed in the $\theta$= $\dfrac{\pi}{2}$ plane as shown in figure. The elements have equal amplitude excitation with 180° polarity difference, operating at wavelength $\lambda$. The correct value of the magnitude of the far-zone resultant electric field strength normalized with that of a single element, both computed for $\phi$= 0, is