A cylinder of radius $R$ and length $L$ is placed in a uniform electric field $E$ parallel to the cylinder axis. The total flux for the surface of the cylinder is given by

A linear charge rod having linear charge density $\lambda$ penetrates a cube diagonally and then, it penetrates a sphere diametrically as shown. What will be the ratio of flux coming out of cube and sphere?

A ring of radius $R$ is placed in the plane with its centre at origin and its axis along the $x$ axis and having uniformly distributed positive charge. A ring of radius $r\left(\ll R\right)$ and coaxial with the larger ring is moving along the axis with constant velocity. Then, the variation of electric flux $\varphi$ passing through the smaller ring with position will be best represented by,

A positive point charge $Q$is placed (on the axis of the disc) at a distance of $4R$above the center of a disc of radius $R$as shown in situation $I.$The magnitude of electric flux through the disc is $\varphi .$Now, a hemispherical shell of a radius $R$is placed over the disc such that it forms a closed surface as shown in situation $\mathrm{II}.$The flux through the curved surface in the situation $\mathrm{II}$ taking direction of area vector along outward normal as positive is

Figure shows, in cross section, three solid cylinders, each of length $L$ and uniform charge $Q$. Concentric with each cylinder is a cylindrical Gaussian surface, with all three surfaces having the same radius. Rank the Gaussian surfaces according to the electric field at any point on the surface, greatest first.

Figure shows four solid spheres, each with charge $Q$ uniformly distributed through its volume. The figure also shows a point $P$ for each sphere, all at the same distance from the center of the sphere. Rank the spheres according to the magnitude of the electric field they produce at point $P$.

In the figure, a hemispherical bowl of radius $R$ is shown. Electric field of intensity $E$ is represented in each situation by direction lines.

Figure shows, in cross section, two Gaussian spheres and two Gaussian cubes that are centered on a positively charged particle. Select the correct alternatives.