$A$ sphere of radius $R$ and charge $Q$ is placed inside a concentric imaginary sphere of radius $2R$. The flux associated with the imaginary sphere is

Consider a cylinder of length $L$ and radius $R$ placed in a uniform electric field $E$ such that its axis is parallel to the electric field. The total electric flux associated with the cylinder is .......

$A$ positive charge $q$ is placed at the centre of a neutral hollow cylindrical conducting shell with its cross-section as shown in the figure below. Which one of the following figures correctly indicates the induced charge distribution on the conductor? (Ignore edge effects)

Shown in the figure is a shell made of a conductor. It has inner radius $a$ and outer radius $b$,and carries a total charge $Q$. At its centre is a dipole $\vec{P}$ as shown. In this case,

$A$ charged particle $q$ is placed at the centre $O$ of a cube of side length $L$ $(A, B, C, D, E, F, G, H)$. Another identical charge $q$ is placed at a distance $L$ from $O$, outside the cube, as shown in the figure. The electric flux through the face $BGFC$ is

Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box is $8.0 \times 10^{3} \; N m^{2} / C$.
$(a)$ What is the net charge inside the box?
$(b)$ If the net outward flux through the surface of the box were zero,could you conclude that there were no charges inside the box? Why or why not?