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

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:

In the figure shown, find the ratio of the linear charge densities ${\lambda }_1$ (on semi – infinite straight wire) and ${\lambda }_2$ (on semi – circular part) that is ${\lambda }_1/{\lambda }_2$ so that the field at $O$ is along $y$ direction.

The linear charge density on a dielectric ring of radius $R$ varies with $\mathrm{\theta }$ as $\lambda ={\lambda }_0\mathrm{cos\theta }/2,$ where ${\lambda }_0$ is constant. Find the potential at the center $O$ of the ring (in volt).

The capacitor of an oscillatory circuit is enclosed in $\mathrm{a}$ container. When the container is evacuated, the resonance frequency of the circuit is $10 \mathrm{kHz}$. When the container is filled with $\mathrm{a}$ gas, the resonance frequency changes by $50 \mathrm{Hz}$. The dielectric constant of the gas is $\frac{x}{100}$. What is the value of $x$?

A circular disc of radius $\mathrm{R}$ carries surface charge density $\sigma \left(\mathrm{r}\right)={\sigma }_0\left(1-\frac{\mathrm{r}}{\mathrm{R}}\right),$ where ${\sigma }_0$ is a constant and $\mathrm{r}$ is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is ${\varphi }_0.$Electric flux through another spherical surface of radius $\frac{\mathrm{R}}{4}$ and concentric with the disc is $\varphi .$ Then the ratio is $\frac{{\varphi }_0}{\varphi }=\frac{x}{5}$, the value of $x$ is___

In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance $C$. The switch $S_1$ is pressed first to fully charge the capacitor $C_1$ and then released. The switch $S_2$ is then pressed to charge the capacitor $C_2$. After some time, $S_2$ is released and then $S_3$ is pressed. After some time,

In the given circuit diagram, $E=12 \mathrm{V}, C_1=4 \mathrm{\mu F}, C_2=2 \mathrm{\mu F}$, $C_3=6 \mathrm{\mu F}$ and $C_4=3 \mathrm{\mu F}$. Find the heat produced in the circuit (in $\mathrm{\mu J}$) after switch $S$ is shorted.

Let $C$ be the capacitance of a capacitor discharging through a resistor $R$. Suppose $t_1$ be the time taken for the energy stored in the capacitor to reduce to half its initial value and $t_2$ be the time taken for the charge to reduce to one-fourth of its initial value. Then the ratio $\frac{t_1}{t_2}$ will be,