Consider an electric field $$\overrightarrow E = {E_0}\widehat x$$ where $${E_0}$$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is

A $$2$$ $$\mu F$$ capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch $$S$$ is turned to position $$2$$ is

A spherical metal shell A of radius $${R_A}$$ and a solid metal sphere $$B$$ of radius $${R_B}\left( { < {R_A}} \right)$$ are kept far apart and each is given charge $$' + Q'.$$ Now they are connected by a thin metal wire. Then