Gauss's 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:

A sphere of radius $10 \mathrm{cm}$ is given a charge of $20 \mathrm{\mu C}$ on its surface. The surface charge density of sphere is

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.

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $\mathrm{R},$with distance $\mathrm{r}$ from the centre $\mathrm{O}$ is represented by:

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

When two conducting spheres are placed at a distance from each other and connected with a wire then will sphere $1$ produce a field at the centre of sphere $2$?

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

The flux passing through the curved surface of the frustum is as shown in the figure. If a charge $Q$ is $R$ distance below the top, then:

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

A solid sphere of radius $R$ carries a positive charge $Q$ distributed uniformly throughout its volume. A very thin hole is drilled through it's center. A particle of mass $m$ and charge $-q$ performs simple harmonic motion about the center of the sphere in this hole. The frequency of oscillation is

A sphere has a positive charge. Figure shows variation of electric field $\left(E\right)$ with distance $x$ from its centre. Which of the following statements is incorrect?

Is Gauss's law valid for the gravitational fields also?

Prove Coulomb's Law from Gauss Law.

State Gauss's law with diagrammatic representation.