Problems For Practice

A uniform electric field $\overrightarrow{E}=E_x\hat{i} \mathrm{N}/\mathrm{C}$ for $x>0$ and $\overrightarrow{E}=-E_x\hat{i} \mathrm{N}/\mathrm{C}$ for $x<0$ are given. A right circular cylinder of length $l \mathrm{cm}$ and radius $r \mathrm{cm}$ has its centre at the origin and its axis along the x-axis. Find out the net outward flux. Using Gauss's law write the expression for the net charge within the cylinder. 

A particle of mass $5\times {10}^{-6}\mathrm{g}$ is kept over a large horizontal sheet of charge density $4\times {10}^{-6}{\mathrm{Cm}}^{-2}$. What charge should be given to this particle, so that if released, it does not fall down. How many electrons should be removed to give this charge?

An infinite line charge produces a field of $9\times {10}^4 {\mathrm{NC}}^{-1}$ at a distance of $4 \mathrm{cm}$. Calculate the linear charge density.

A cylinder of large length carries a charge of $2\times {10}^{-8}{\mathrm{Cm}}^{-1}$. Find the electric field at a distance of $0.2 \mathrm{m}$ from it.

An infinitely long wire is stretched horizontally $4$ metre above the surface of the earth. It carries a charge $1 \mathrm{\mu C}$ per cm of its length. Calculate its electric field at a point on the earth's surface vertically below the wire.

Two large metal plates each of area $1 {\mathrm{m}}^2$ are placed facing each other at a distance of $10 \mathrm{cm}$ and carry equal and opposite charges on their faces. If the electric field between the plates is $100 {\mathrm{NC}}^{-1}$, find the charge on each plate.

An electron is revolving around a long line charge having charge density $2\times {10}^{-8}\mathrm{C} {\mathrm{m}}^{-1}$. Find the kinetic energy of the electron, assuming that it is independent of the radius of electron's orbit.

A spherical shell of metal has a radius of $0.25 \mathrm{m}$ and carries a charge of $0.2 \mathrm{\mu C}$. Calculate the electric field intensity at a point (i) inside the shell, (ii) just outside the shell and (iii) $3.0 \mathrm{m}$ from the centre of the shell.