GATE EC 2017 Set 2 Q27 — Maxwell's Equations

A square metal sheet of $4 \mathrm{~m} \times 4 \mathrm{~m}$ is placed on the $x-y$ plane as shown in the figure below. If the surface charge density (in $\mu \mathrm{C} / \mathrm{m}^{2}$ ) on the sheet is $\rho_{s}(x, y)=4\mid y \mid$, then the total charge (in $\mu \mathrm{C}$, rounded off to the nearest integer) on the sheet is $\_\_\_\_\_\_$

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

In the table shown, List I and List II, respectively, contain terms appearing on the left-hand side and the right-hand side of Maxwell’s equations (in their standard form). Match the left-hand side with the corresponding right-hand side. …

In the circuit shown, $V_{s}$ is square wave of period $T$ with maximum and minimum values of $8\: V$ and $-10\: V$, respectively. Assume that the diode is ideal and $R_{1}=R_{2}=50\: \Omega.$ The average value of $V_{L}$ is _______ volts (rounded off to $1$ decimal place).

Two conducting spheres $S1$ and $S2$ of radii $a$ and $b$ ($b>a$) respectively, are placed far apart and connected by a long, thin conducting wire, as shown in the figure. For some charge placed on this structure, the potential and surface electric field on $S1$ are $V_a$ and $E_a$ and that on S2 are $V_b$ and $E_b$, respectively. …

Concentric spherical shells of radii $2$m, $4$m, and $8$ m carry uniform surface charge densities of $20 \: nC/m^2$, $– 4 \: nC/m^2$ and $\rho_s$ respectively. The value of $\rho_s$ ($nC/m^2$) required to ensure that the electric flux density $\overrightarrow D$ = $\overrightarrow 0$ at radius $10$ m is ________