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 $\vec{F}_1 = A(\hat{i}y + \hat{j}x)$ and $\vec{F}_2 = A(\hat{i}y − \hat{j}x)$?

In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amperes) through the resistor is 2sin(t + $$\pi$$/2). The displacement current (in Amperes) through the capacitor is __________.

In an electrostatic field, the electric displacement density vector, $$\overrightarrow D $$, is given by

$$\overrightarrow D (x,y,z) = ({x^3}\overrightarrow i + {y^3}\overrightarrow j + x{y^2}\overrightarrow k )$$ C/m^{2},

where, $$\overrightarrow i $$, $$\overrightarrow j $$, $$\overrightarrow k $$ are the unit vectors along x-axis, y-axis, and z-axis, respectively. Consider a cubical region R centered at the origin with each side of length 1 m, and vertices at ($$\pm$$ 0.5 m, $$\pm$$ 0.5 m, $$\pm$$ 0.5 m). The electric charge enclosed within R is __________ C (rounded off to two decimal places).

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, which of the following is CORRECT?