B M Sharma Solutions for Chapter: Coulomb's Law and Electric Field, Exercise 8: Archives

Let $\left[{\epsilon }_0\right]$ denote the dimensional formula of the permittivity of vacuum. If $M=$ mass, $L=$ length, $T=$ time and $A=$ electric current, then:

A long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $-\sigma$ in the lower half. The electric field lines around the cylinder will look like figure given in: (figures are schematic and not drawn to scale)

An electric dipole has a fixed dipole moment $\overrightarrow{p}$ which makes angle $\mathrm{\theta }$ with respect to $x$-axis. When subjected to an electric field ${\overrightarrow{E}}_1=E\hat{\mathrm{i}}$, it experiences a torque ${\overrightarrow{T}}_1=\tau \hat{\mathrm{k}}$. When subjected to another electric field ${\overrightarrow{E}}_2=\sqrt{3}E\hat{\mathrm{j}}$, it experiences torque ${\overrightarrow{T}}_2=-{\overrightarrow{T}}_1$. The angle $\mathrm{\theta }$ is, 

A tiny spherical oil drop carrying a net charge $q$ is balanced in still air with a vertical uniform electric field of strength $\left(\frac{81\pi }{7}\right)\times {10}^5 \mathrm{V} {\mathrm{m}}^{-1}.$ When the field is switched off, the drop is observed to fall with terminal velocity $2\times {10}^{-3}{ \mathrm{m} \mathrm{s}}^{-1}.$ Given $g=9.8{ \mathrm{m} \mathrm{s}}^{-2},$ the viscosity of the air is $1.8\times {10}^{-5} \mathrm{N} \mathrm{s} {\mathrm{m}}^{-2},$ and the density of oil is $900 \mathrm{kg}{ \mathrm{m}}^{-3},$ the magnitude of $q$ is:

A wooden block performs SHM on a frictionless surface with frequency ${\nu }_0$. The block carries a charge $+Q$ on its surface. If a uniform electric field $E$ is switched on as shown, then the SHM of the block will be

A few electric field lines for a system of two charges $Q_1$ and $Q_2$, fixed at two different points on the $x$-axis are shown in the figure. These lines suggest that

Four charges $Q_1, Q_2, Q_3$ and $Q_4$ of same magnitude are fixed along the $x$ axis at $x=-2a, -a, +a$ and $+2a,$ respectively. $A$ positive charge $q$ is placed on the positive $y$ axis at a distance $b>0.$ Four options of the signs of these charges are given in List I. The direction of the forces on the charge $q$ is given in List II. Match List I with List II and select the correct answer using the code given below the lists.

A particle of mass ${10}^{-3} \mathrm{kg}$ and charge $1.0 \mathrm{C}$ is initially at rest. At time $t=0,$ the particle comes under the influence of an electric field $\overrightarrow{E}\left(t\right)=E_0\sin \left(\omega t\right)\hat{\mathrm{i}}$, where $E_0=1.0 \mathrm{N} {\mathrm{C}}^{-1}$ and $\omega ={10}^3 \mathrm{rad} {\mathrm{s}}^{-1}.$ Consider the effect of only the electrical force on the particle. Then the maximum speed in $\mathrm{m} {\mathrm{s}}^{-1}$ attained by the particle at subsequent times is: