Gauss's Theorem and Its Applications

Which law is used to derive the expression for the electric field between two uniformly charged large parallel sheets with surface charge densities $\sigma$ and $-\sigma$ respectively:

Applying Gauss theorem, the expression for the electric field intensity at a point due to an infinitely long, thin, uniformly charged straight wire is

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:

When the charge on a capacitor increases keeping geometry the same

An $100\mathrm{eV}$ electron is fired directly towards a large metal plate having surface charge density $-2\times {10}^{-6}{ \mathrm{C} \mathrm{m}}^{-2}$. The distance from where the electron be projected so that it just fails to strike the plate is

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 total flux through the faces of the cube with side of length $\mathrm{\alpha }$ if a charge $\mathrm{q}$ is placed at corner $\mathrm{A}$ of the cube is

A point charge of $1.8 \mathrm{\mu C}$ is at the centre of cubical Gaussian surface$55 \mathrm{cm}$ on edge. What is the net electric flux through the surface?

A ring of radius $R$ having a linear charge density $\lambda$ moves towards a solid imaginary sphere of radius $\frac{R}{2},$ so that the centre of ring passes through the centre of the sphere. The axis of the ring is perpendicular to the line joining the centres of the ring and the sphere. The maximum flux through the sphere in this process is

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

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

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

$q_1,\mathrm{ }{q}_2,\mathrm{ }{q}_3$ and $q_4$ are point charges located at points, as shown in the figure, and $S$ is a spherical Gaussian surface of radius $R$. Which of the following is true, according to the Gauss' law?

The figure shows a closed surface which intersects a conducting sphere. If a positive charge is placed at the point $P$, the flux of the electric field through the closed surface, 

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 hollow cylinder has a charge $q \mathrm{coulomb}$ at the middle point of it. If $\mathrm{\varphi }$ is the electric flux in units of volt metre associated with the curved surface $B$, the flux linked with the plane surface $A$ in a unit of volt metre will be

The potential due to an electrostatic charge distribution is $V\left(r\right)=\frac{q{e}^{-\alpha r}}{4\pi {\epsilon }_{0}r},$ where $\alpha$ is positive. The net charge within a sphere centred at the origin and of radius $1/\alpha$ is

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