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 __________.
Consider the following wave equation,
$${{{\partial ^2}f(x,t)} \over {\partial {t^2}}} = 10000{{{\partial ^2}f(x,t)} \over {\partial {x^2}}}$$
Which of the given options is/are solution(s) to the given wave equation?
A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of 10$$-$$4 cm, with air as the dielectric. Assume the speed of light in air to be 3 $$\times$$ 108 m/s. The frequency/frequencies of TM waves which can propagate in this waveguide is/are ___________.
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/m2,
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).