A square metal sheet of $4\text{ m} \times 4\text{ m}$ is placed on the $x-y$ plane as shown in the figure below. !image(https://uadmin.udsfgecw.tech/file/download/public/public:66560c79-4a7a-47be-b4dc-4038a52ad9c8.jpg) If the surface charge density (in $\mu\text{C}/\text{m}^2$) on the sheet is $\rhos(x, y) = 4|y|$, then the total charge (in $\mu\text{C}$, rounded off to the nearest integer) on the sheet is

An electric field of $0.01 \text{ V/m}$ is applied along the length of a copper wire of circular cross-section with diameter $1 \text{ mm}$. Copper has a conductivity of $5.8 \times 10^7 \text{ S/m}$. The current (in Amperes, rounded off to two decimal places) flowing through the wire is .

Let $\hat{i}$ and $\hat{j}$ be the unit vectors along $x$ and $y$ axes, respectively and let $A$ be a positive constant. Which one of the following statements is true for the vector fields $\vec{F}1 = A(y\hat{i} + x\hat{j})$ and $\vec{F}2 = A(y\hat{i} - x\hat{j})$?

A lossless transmission line with characteristic impedance $Z0 = 50\ \Omega$ is terminated with an unknown load. The magnitude of the reflection co-efficient is $|\Gamma| = 0.6$. As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in $\Omega$) is .

A uniform plane wave with electric field $\vec{E}(x) = Ay \hat{a}y e^{-j \frac{2\pi x}{3}}$ V/m is travelling in the air (relative permittivity, $\varepsilonr = 1$ and relative permeability, $\mur = 1$) in the $+x$ direction ($Ay$ is a positive constant, $\hat{a}y$ is the unit vector along the $y$ axis). It is incident normally on an ideal electric conductor (conductivity, $\sigma = \infty$) at $x = 0$. The position of the first null of the total magnetic field in the air (measured from $x = 0$, in metres) is .