The electric field near a conducting surface having a uniform surface charge density $\sigma$ is given by,

An infinite line charge produces a field of $4.5\times {10}^4 \mathrm{N} {\mathrm{C}}^{-1}$ at a distance $2 \mathrm{m}$ from it. The linear charge density is

The electric potential inside a conducting sphere

For a point situated at a distance $20 \mathrm{cm}$ from the axis of a long cylindrical charged conductor, the electric intensity is $0.4 \mathrm{N} {\mathrm{C}}^{-1}$. The electric intensity at another point situated at $40 \mathrm{cm}$ from the axis is

The maximum charge that can be conveyed to a conducting sphere of diameter $20 \mathrm{cm}$ (breakdown field of air $=2\times {10}^6 \mathrm{V} {\mathrm{m}}^{-1}$) is

Two conducting spheres of radii $r_{1}$ and $r_{2}$ are charged to the same surface charge density. The ratio of electric field near their surface is

A charge $Q=1.8 \mu \mathrm{C}$ is placed at the centre of a cube of edge $55 \mathrm{cm}$. The electric flux through one of the faces of the cube is

The electric field in a region is radially outward with magnitude $E=\frac{A}{{\gamma }_0}$. The charge contained in a sphere of radius ${\gamma }_0$, centered at the origin is

Cylinder is charged by $10 \mathrm{mC}$. Length of cylinder is $1 \mathrm{km}$ and radius is $1 \mathrm{mm}$. Surface charge density of cylinder is