The surface charge density of a conductor is $12\times {10}^{-12} {\mathrm{cm}}^{-2}$. If the conductor is surrounded by a medium of dielectric constant $3.14$, the magnitude of electric field just outside the conductor is $\left(\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9 {\text{N m}}^2 {\mathrm{C}}^{-2}\right)$

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 spheres $A$ and $B$ are having radii $5 \mathrm{cm} \text{and} 10 \mathrm{cm}$ and carrying charges of $+5 \mathrm{C} \text{and}+15 \mathrm{C}$, respectively, distributed uniformly. Their centres are separated by $80 \mathrm{cm}$. The electric field on the line joining the centres of the spheres will be zero at a distance from the centre of $A$ equal to

A conducting sphere of radius $0.1 \mathrm{m}$ has a uniform positive charge density of $1.8 \mu \mathrm{C}/{\mathrm{m}}^2$ on its surface. The electric field in $\mathrm{V}/\mathrm{m}$ in free space at a radial distance of $0.2 \mathrm{m}$ from a point on the surface of the sphere is given by

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

A metal of surface area $1 {\mathrm{m}}^2$ is charged with $\sqrt{8.85} \mu \mathrm{C}$ in air. The mechanical force acting on it is (Use:${\epsilon }_0=8.85\times {10}^{-12} \mathrm{F} {\mathrm{m}}^{-1}$