S L Arora Solutions for Chapter: Electric Charges and Field, Exercise 1: 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. 

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 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?

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.