Embibe Experts Solutions for Chapter: Electrostatics, Exercise 2: Level 2

An electric field is given by $\overrightarrow{E}=\left(y\hat{\mathrm{i}}+x\hat{\mathrm{j}}\right) \mathrm{N} {\mathrm{C}}^{-1}$. Find the work done (in $\mathrm{J}$) in moving a $1 \mathrm{C}$ charge from ${\overrightarrow{r}}_{\mathrm{A}}=\left(2\hat{\mathrm{i}}+2\hat{\mathrm{j}}\right) \mathrm{m}$ to ${\overrightarrow{r}}_{\mathrm{B}}=\left(4\hat{\mathrm{i}}+\hat{\mathrm{j}}\right) \mathrm{m}$

The arrangement is shown consists of three elements.
a. A thin rod of charge $-3.0 \mu \mathrm{C}$ that forms a full circle of radius $6.0 \mathrm{cm}.$
b. A second thin rod of charge $2.0 \mu \mathrm{C}$ that forms a circular arc of radius $4.0 \mathrm{cm}$ and concentric with the full circle, subtending an angle of $90°$ at the centre of the full circle.
c. An electric dipole with a dipole moment that is perpendicular to a radial line and has magnitude $1.28\times {10}^{-21} \mathrm{C} \mathrm{m}$
Find the net electric potential in volts at the centre.

The point charges $-2q,-2q$ and $+q$ are put on the vertices of an equilateral triangle of side $a.$ Find the work done by some external force in increasing the separation to $2a$ (in joules).

A parallel plate capacitor is to be constructed which can store $q=10 \mathrm{\mu C}$ charge at $V=1000 \mathrm{V}$ . The minimum plate area of the capacitor is required to be $A_1$ when space between the plates has air. If a dielectric of constant $K=3$ is used between the plates, the minimum plate area required to make such a capacitor is $A_2$. The breakdown field for the dielectric is $8$ times that of air. Find $\frac{A_1}{A_2}.$

Find the amount by which the total energy stored in the capacitor (in $\mu \mathrm{J}$) will increase in the circuit shown in the figure after the switch $K$ is closed. Consider all capacitors are of capacitance $3 \mathrm{\mu F}$ and battery voltage is $10 \mathrm{V}$.

For section $AB$ of a circuit shown in figure, $C_1=1 \mathrm{\mu F},C_2=2 \mathrm{\mu F},E=10 \mathrm{V}$, and the potential difference $V_A-V_B=-10 V$. Charge on capacitor $C_1$ is:

Find the charge (in $\mu \mathrm{C}$) on the capacitor $\mathrm{C}$ in the figure shown. Internal resistance of a source is to be neglected. (Take : $\mathcal{E}=9 \mathrm{V}, C=2\mu \mathrm{F}$)

In the circuit shown in figure, the capacitors are initially uncharged. The current through resistor $PQ$ just after closing the switch is,