Gauss' Law

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:

The number of electric lines of force that radiate outwards from one coulomb of charge in vacuum is

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : If an electric dipole of dipole moment $30\times {10}^{–5} \mathrm{C} \mathrm{m}$ is enclosed by a closed surface, the net flux coming out of the surface will be zero.

Reason R : Electric dipole consists of two equal and opposite charges.

In the light of above, statements, choose the correct answer from the options given below.

A charge $20 \mathrm{\mu C}$is enclosed by a Gaussian spherical surface of radius $10 \mathrm{cm}$. If the radius is doubled, then outward electric flux will

If the charge given to an insulated sphere behaves as the whole charge is at the centre of sphere then the observation point is -
(1) outside the surface
(2) on the surface
(3) outside or on the surface
(4) at the centre

In a uniform electric field find the total flux associated with the given surfaces

A closed spherical surface encloses a charge $q$ at its centre. Show that the electric flux through the closed surface is $\frac{q}{{\epsilon }_0}$.

At what distance from the centre of ring on axis, electric field is maximum :-

Five electric dipole of charge 'q' each are placed into the shell. What will be the amount of electric flux associated with shell?

A charge q is located at the centre of a cube. The electric flux through any two consecutive faces will be

Figure shows two uniform charged concentric spherical shells. Both the charges are positive. Select the correct statement.

In a region of space, the electric filed $\overrightarrow{E}=E_{0}x\hat{\mathrm{i}}+E_{0}y\hat{\mathrm{j}}$, Consider imaginary cubical volume of edge $a$ with its edges parallel to the axes of coordinates. Now

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The nuclear charge $\left(Ze\right)$ is non-uniformly distributed within a nucleus of radius $R$. The charge denity $\rho \left(r\right)$ [charge per unit volume] is dependent on the radial distance $r$ from the centre of the nucleus as shown in figure. Select conrect alternative/s.

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Find the electric flux through a closed surface S shown in the diagram.

In the figure, the inner (shaded) region $A$ represents a sphere of radius $r_A=1$, within which the electrostatic charge density varies with the radial distance $r$ from the center as ${\rho }_A=kr$, where $k$ is positive. In the spherical shell $B$ of outer radius $r_B$, the electrostatic charge density varies as ${\rho }_B=\frac{2k}{r}$. Assume that dimensions are taken care of. All physical quantities are in their SI units.

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Which of the following statement(s) is/(are) correct?

Prove Coulomb's Law from Gauss Law.

State Gauss's law with diagrammatic representation.

A charge $Q$ is placed at the mouth of a conical flask. The flux of the electric field through the flask is

A point charge '$q$' is placed at a distance '$l$' (on the $y$-axis) vertically above the surface which lies in the $xz$ plane as shown in the figure. The flux of electric field passing through the shaded portion is $\frac{\lambda q}{48{\epsilon }_0}$. Find the value of $\lambda$.

$4500$ flux lines are going inside an area of ​​a certain volume and $2500$ flux lines are passing through that area are going out. How much charge is there within that field?