Gauss’s Law

The SI unit of electrical flux is:

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

The charge density of uniformly charged infinite plane is $\sigma$. A simple pendulum is suspended vertically downward near it. Charge $q_0$ is placed on metallic bob. If the angle made by the string is $\theta$ with vertical direction then _____

If charge $q$ is placed on one of the vertex of a cube. Then flux passing through any one surface of cube 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:

An electric field $\mathrm{E}$ is present ${\perp }^{\mathrm{r}}$ to a square plate of side length $\mathrm{L}$. What is the flux passing through the plate?

A charge $\mathrm{Q}$ is distributed uniformly in a sphere (solid). Then the electric field at any point $\mathrm{r}$, where $\mathrm{r}<\mathrm{R}$ ( $\mathrm{r}$ is radius of sphere) varies as_____.

Two infinitely long parallel conducting plates having surface charge densities $+\mathrm{\sigma }$ and $-\mathrm{\sigma }$ respectively are separated by a small distance. The medium between the plates is vacuum, if ${\mathrm{\epsilon }}_{\mathrm{o}}$ is dielectric permittivity of vacuum, then the electric field in the region between the plates is-

A cylinder of radius $R$ and length $L$ is placed in a uniform electric field $E$ parallel to the cylinder axis. The total flux for the surface of the cylinder is given by

$\oint \overrightarrow{E.}\overrightarrow{ds}=\frac{Q_{net}}{{\epsilon }_o}$

E signifies the _____ passing through a certain area dS. $Q_{net}$ is the total amount of charge and ${\epsilon }_o$signifies the permittivity of the vacuum.

Derive Gauss's law from Coulomb's law.

A hollow cylinder has a charge $q$ coulomb within it. If $\varphi$ is the electric flux in units of $\mathrm{Volt} \mathrm{meter}$ associated with the curved surface $\mathrm{B}$, the flux linked with the plane surface $\mathrm{A}$ in units of $\mathrm{Volt} \mathrm{meter}$ will be

The $\mathrm{ }\mathrm{S}\mathrm{I}$ unit of electric flux is:

A parallel plate capacitor has two square plates with equal and opposite charges. The surface charge densities on the plates are $+\mathrm{\sigma }$ and $–\mathrm{\sigma }$ respectively. In the region between the plates the magnitude of the electric field is

The potential (in volts) of a charge distribution is given by

$V\left(z\right)=30-5z^2$ for $\left|z\right|\le 1\mathrm{ }\mathrm{m}$

$V\left(z\right)=35-10\mathrm{ }\left|\mathrm{z}\right|$ for $\left|Z\right|\ge 1\mathrm{ }\mathrm{m}$ .

$V\left(z\right)$ does not depend on $x$ and $y$. If this potential is generated by a constant charge per unit volume ${\mathrm{\rho }}_0$ (in units of ${\mathrm{ϵ}}_0$ ) which is spread over a certain region, then choose the correct statement.

The $\mathrm{ }\mathrm{S}\mathrm{I}$ unit of electric flux is:

The ratio of electric field intensity at $\mathrm{P}$ & $\mathrm{Q}$ in the shown arrangement is

A charge $Q$ is placed at a distance $\raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ above the centre of a square surface of side length $a$. The electric flux through the square surface due to the charge would be?