Gauss Law

A hollow charged metal sphere has radius $r$. If the potential difference between its surface and a point at a distance $3r$ from the centre is$V$, then electric field intensity at a distance $3r$ is:

What is the electric field inside a charged conductor ? Plot a graph between electric field strength $\mathrm{E}$ and distance from centre in case of a charged conducting sphere of radius $\mathrm{R}$.

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.

A Gaussian sphere encloses an electric dipole within it. The total flux through the sphere is

Flux coming out from a unit positive charge enclosed in air is

A conducting spherical shell of radius $R$ has a charge $+q$units. The electric field due to the shell at a point

A non conducting solid cylinder of infinite length having uniform charge density $\rho$ and radius of cylinder is $5R$. Find the flux passing through the surface $ABCD$ as shown in figure.

State Gauss' theorem in electrostatics and write its expression.

The electric potential at the surface of a charged spherical conductor of radius $10 \mathrm{cm}$ is $15 \mathrm{V}$. Electric potential at its centre in volt is 

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?

A large uniformly charged sheet having a surface charge density of $5\times {10}^{-16} \mathrm{C}/{\mathrm{m}}^2$ lies in $\mathrm{X}-\mathrm{Y}$ plane. Calculate the electric flux through a circular loop of radius $0.1 \mathrm{m},$ whose axis makes on angle of $60°$ with $Z$ axis.

A particle of mass $9\times {10}^{-5} \mathrm{gm}$ is placed at some height above a uniformly charged horizontal infinite non conducting plate having a surface charge density $5\times {10}^{-5} \mathrm{C}/{\mathrm{m}}^2$. What should be the charge on the particle so that on releasing it will not fall down. Take, $g=9.8 \mathrm{m}/{\mathrm{s}}^2$

Two metallic plates each of area is $1 {\mathrm{m}}^2$ placed parallel to each other at a separation of $0.05 \mathrm{m}$. Both have charges of equal magnitude but of opposite nature. If the magnitude of electric field in space between them is $5.5 \mathrm{V}/\mathrm{m}$, then calculate the magnitude of charge on each plate.

A charge of $10 \mathrm{\mu C}$ is given to a metallic plate of area ${10}^{-2} {\mathrm{m}}^2$. Determine the intensity of electric fields at points near by.

A charge of $10 \mathrm{\mu C}$ is placed directly above the centre of a square of $10 \mathrm{cm}$ side at a height of $5 \mathrm{cm}$ as shown in the figure. Determine the magnitude of electric flux through the square?

An infinite line charge produces an electric field of $9\times {10}^4 \mathrm{N}/\mathrm{C}$ at $2 \mathrm{cm}$ from it. Determine the linear charge density.

The intensity of electric field due to a charged sphere at a point at a distance of $20 \mathrm{cm}$ from in centre is $10 \mathrm{V}/\mathrm{m}$. The radius of sphere is $5 \mathrm{cm}$. Determine the intensity of electric field at a distance of $8 \mathrm{cm}$ from the centre.

Consider a cube of side $a$, Let a charge $q$ be placed at one face of the cube. Calculate the total flux linked with cube and comment on the flux linked with each face.

Consider a cube of side $a$, Let a charge $q$ be placed at one corner of cube. Calculate the total flux linked with cube and flux linked with each face.