Applications of Gauss's Law

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:

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

Two conducting spheres of radii $r_1$ and $r_2$ have equal surface charge densities. The ratio of their charges is ___.

The electric potential at the surface of a charged spherical conductor of radius $10 \mathrm{cm}$ is $15 \mathrm{V}$. Electric potential at its centre in volt is 

An electron of ${10}^{3 }\mathrm{eV}$ energy is fired from a distance of $5 \mathrm{mm}$ perpendicularly towards an infinite charged conducting plate. What should be the minimum charge density on plate so that electron fails to strike the plate?

A particle of mass $9\times {10}^{-5} \mathrm{gm}$ is placed at some height above a uniformly charged horizontal infinite non conducting plate having a surface charge density $5\times {10}^{-5} \mathrm{C}/{\mathrm{m}}^2$. What should be the charge on the particle so that on releasing it will not fall down. Take, $g=9.8 \mathrm{m}/{\mathrm{s}}^2$

Two metallic plates each of area is $1 {\mathrm{m}}^2$ placed parallel to each other at a separation of $0.05 \mathrm{m}$. Both have charges of equal magnitude but of opposite nature. If the magnitude of electric field in space between them is $5.5 \mathrm{V}/\mathrm{m}$, then calculate the magnitude of charge on each plate.

A charge of $10 \mathrm{\mu C}$ is given to a metallic plate of area ${10}^{-2} {\mathrm{m}}^2$. Determine the intensity of electric fields at points near by.

An infinite line charge produces an electric field of $9\times {10}^4 \mathrm{N}/\mathrm{C}$ at $2 \mathrm{cm}$ from it. Determine the linear charge density.

The intensity of electric field due to a charged sphere at a point at a distance of $20 \mathrm{cm}$ from in centre is $10 \mathrm{V}/\mathrm{m}$. The radius of sphere is $5 \mathrm{cm}$. Determine the intensity of electric field at a distance of $8 \mathrm{cm}$ from the centre.

Consider two infinite parallel planes having charge densities $+\sigma$ and $-\sigma$ respectively. What is the magnitude of the electric field at some point in the region between them?

Consider two long straight line charges having linear charge densities ${\lambda }_1$ and ${\lambda }_2$. Derive expression for the force per unit length acting between them.

Graph the variation of electric field with distance for a uniformly charged non-conducting sheet.

Write the expression for force per unit area on a charged spherical conductor and give its direction.

Electric field intensity due to a long straight charged wire varies with $\frac{\mathit{1}}{\mathit{r}}$as shown in 

What was the main cause of the Deccan Riots of 1875?

Where did Gautama Buddha attain enlightenment?

What was the impact of the British land revenue policies on Indian peasants?

What was the main objective of the British land revenue system in India?