Normal Electric Induction and Gauss' Theorem

A sphere of radius $10 \mathrm{cm}$ is given a charge of $20 \mathrm{\mu C}$ on its surface. The surface charge density of sphere is

A charge of $5\times {10}^{-10} \mathrm{C}$ is given to a metal cylinder of length $10 \mathrm{cm}$ placed in air. The electric intensity due to the cylinder at a distance $0.2 \mathrm{m}$ from the axis is

Where do electric field lines point?

Is electric field intensity a vector quantity?

What is electric field intensity?

Why the electric field just outside the surface of a conductor is normal to the surface?

Assertion: Gauss's law can't be used to calculate electric field near an electric dipole.
Reason: Electric dipole don't have symmetrical charge distribution.

Gauss law is applicable only when there is a symmetric distribution of charge.

In the figure shown, there is a large sheet of charge of uniform surface charge density $\sigma$. A charge particle of charge $-q$ and mass $m$ is projected from a point $A$ on the sheet with a speed $u$ with angle of projection such that it lands at maximum distance from $A$ on the sheet. Neglecting gravity, find the time of flight.

The electric field intensity outside the charged conducting sphere of radius $‘R’$, placed in a medium of permittivity $\epsilon$ at a distance $‘r’$ from the centre of the sphere in terms of surface charge density $\sigma$ is

A metal sphere of radius $1 \mathrm{cm}$ is charged with $3.14 \mathrm{\mu C}$. Find the electric intensity at a distance of $1 \mathrm{m}$ from the centre of the metal sphere.

A long cylinder of radius $2 \mathrm{cm}$ carries a charge of $5 \frac{\mathrm{\mu C}}{\mathrm{m}}$ kept in a medium of dielectric constant $10$. Find the electric field intensity at a point situated at a distance of $1 \mathrm{m}$ from the axis of cylinder.

Two conducting spheres of radii $r_1$ and $r_2$ have equal surface charge densities. The ratio of their charges is ___.

The radii of two conducting spheres are $a$ and $b$. When these are given same surface charge density the ratio of electric field intensities at their surfaces is 

Derive an expression for electric field intensity at a point close and outside the surface of charged conductor of any shape.

Obtain an expression for electric field intensity at a point outside infinitely long charged conducting cylinder.

Obtain an expression for electric field intensity at a point outside a charged conducting sphere.

State Gauss' theorem in electrostatics and write its expression.

The electric potential at the surface of a uniformly charged non-conducting sphere of radius $5 \mathrm{cm}$ is $10 \mathrm{V}$. What is the electric field(in $\mathrm{V} {\mathrm{m}}^{-1}$) at its centre.

An electron of ${10}^{3 }\mathrm{eV}$ energy is fired from a distance of $5 \mathrm{mm}$ perpendicularly towards an infinite charged conducting plate. What should be the minimum charge density on plate so that electron fails to strike the plate?