Embibe Experts Solutions for Chapter: Electrostatics, Exercise 3: Exercise - 3

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

A charge $Q$ is uniformly distributed over a long rod $\mathrm{AB}$ of length $L$ as shown in the figure. The electric potential at the point $O$ lying at distance $L$ from the end $\mathrm{A}$ is

Assume that an electric field $\stackrel{\rightharpoonup }{E}=\left(30{\mathrm{x}}^2\hat{\mathrm{i}}\right) \mathrm{N} {\mathrm{C}}^{-1}$ exists in space. Then the potential difference $V_A – V_O,$ where $V_O$ is the potential at the origin and $V_A$the potential at $x=2 \mathrm{m}$ is

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)

A uniformly charged solid sphere of radius $R$ has potential $V_0$ (measured with respect to $\infty$) on its surface. For this sphere the equipotential surfaces with potentials $\frac{3V_0}{2},\frac{{\displaystyle 5V_0}}{{\displaystyle 4}},\frac{{\displaystyle 3V_0}}{{\displaystyle 4}} \text{and} \frac{{\displaystyle V_0}}{{\displaystyle 4}}$ have radius $R_1, R_2, R_3$ and $R_4$, respectively. Then

The region between two concentric spheres of radii $a$ and $b$, respectively (see figure), has volume charge density $\rho =\frac{A}{r}$, where $A$ is a constant and $r$ is the distance from the centre. At the centre of the spheres is a point charge $Q$. The value of $A$ such that the electric field in the region between the spheres will be constant, is

An electric dipole has a fixed dipole moment $\stackrel{\rightharpoonup }{p}$ , which makes angle $\theta$ with respect to $x-$axis. When subjected to an electric field ${\overrightarrow{E}}_1=E\hat{\mathrm{i}}$ , it experiences a torque ${\stackrel{\rightharpoonup }{T}}_1=\tau \hat{\mathrm{k}}$. When subjected to another electric field $E_2=\sqrt{3}{E}_1\hat{\mathrm{j}}$ it experiences a torque $T_2=-T_1$. The angle $\theta$ is

Three concentric metal shells $A, B\text{ and} C$ of respective radii $a,b\text{ and} c(a<b<c)$ have surface charge densities $+\mathrm{\sigma }, –\mathrm{\sigma } \text{and} +\mathrm{\sigma }$, respectively. The potential of shell $B$ is,