Gauss’ Law 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:

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.

Let the electrostatic field, $E$ at distance, $r$ from a point charge, $q$ not be an inverse square but instead an inverse cubic, e.g. $E=k\frac{q}{r^3}\hat{r}$, here $k$ is a constant. Consider the following two statements: (I) Flux through a spherical surface enclosing the charge is, $\varphi =\frac{q_{\mathrm{enclosed}}}{{\epsilon }_0}$. (II) A charge placed inside a uniformly charged shell will experience a force. Which of the above statements are valid?

A point electric charge $Q$ is placed at a corner of a cube as shown in the figure. What is the electric flux passing through $ABCD$ of the cube? (${\in }_0$ is permittivity of free space)

A point charge $Q,$ is placed at the center of a cube of side $a,$ in vacuum (permitivity $\left.{ϵ}_0\right).$ The flux of the electric field through the shaded face is given by

A sphere of radius $R$ carries a positive charge density $\left(\rho \right)$ that increases linearly with radial distance $r$ from the centre $(\rho \propto r).$ The radial dependence of the magnitude of electric field inside the sphere is given by

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

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 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?

Consider a uniformly charged solid cylinder of large length and radius $R.$ Now consider a cylindrical surface of radius $2R$ and length $2R$ coaxial with cylinder and electric flux through cylindrical surface is ${\varphi }_0.$ Now consider a spherical surface of radius $2R$ and one of the diameter along axis of cylinder and electric flux through spherical surface is $\varphi .$ Find $10\frac{\varphi }{{\varphi }_0}$ to the nearest integer.

In the shown figure a hemisphere is placed and two charges $3\mathrm{q}$ and $9\mathrm{q}$ are placed symmetrically about centre $O.$ Net electric flux over curved surface is given as $\frac{N_{1}q}{N_2{\epsilon }_0},$ where $N_1$ and $N_2$ are lowest possible integers then value of $N_1+N_2$ is :

The electric field in a region is radially outwards with magnitude $E=\frac{\alpha r}{{ϵ}_0}.$ In a sphere of radius $R$ centered at the origin, calculate the value of charge in coulombs if $\alpha =\frac{5}{\pi }\mathrm{V}/{\mathrm{m}}^2$ and $R={\left(\frac{3}{10}\right)}^{1/3} \mathrm{m}$

A sphere of radius $\mathrm{R}$ have volume charge density given as
$\rho \left(\mathrm{r}\right)=\mathrm{Kr}$ for $\mathrm{r}\le \mathrm{R}$

$=0$ for $\mathrm{r}>\mathrm{R}$
If electric field at distance $\frac{\mathrm{R}}{2}$ from centre is $\frac{{\mathrm{KR}}^2}{2\mathrm{N}{\epsilon }_0}$ Then $\mathrm{N}$ will be.

A point charge of $+12 \mu \mathrm{C}$ is at a distance $6 \mathrm{cm}$ vertically above the centre of a square of side $12 \mathrm{cm}$ as shown in figure. The magnitude of the electric flux through the square will be _________ $\times {10}^3 \mathrm{N} {\mathrm{m}}^2 {\mathrm{C}}^{-1}.$(Write the value to the nearest integer)

A circular disc of radius $R$ carries surface charge density $\sigma \left(r\right)={\sigma }_0\left(1-\frac{r}{R}\right),$ where ${\sigma }_0$ is a constant and r is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is ${\varphi }_0$Electric flux through another spherical surface of radius $\frac{R}{4}$ and concentric with the disc is $\varphi .$ The ratio $\frac{{\varphi }_0}{\varphi }=\frac{x}{5}$, find the value of $x$.

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.