Embibe Experts Solutions for Chapter: Electrostatics, Exercise 1: Exercise 1

A simple pendulum of mass $m$ charged negatively to $q$ coulomb oscillates with a time period $T$ in a downward electric field $E$ such that $mg>qE.$ If the electric field is withdrawn, the new time period

A charged particle $X$ moves directly towards another charged particle $Y$. For the $X$ and $Y$ system, the total momentum is $p$ and the total energy is $E$.

Consider the following conclusions regarding the components of an electric field at a certain point in space given by, $E_{\mathrm{x}}=-Ky\text{,} E_{\mathrm{y}}=Kx\text{,} E_{\mathrm{z}}=0$.

The electric potential in a region along the $x$-axis varies with $x$ according to the relation $V\left(x\right)=4+5x^2$. Then

There are $27$ drops of a conducting fluid. Each drop has radius $r,$ and each of them is charged to the same potential $V_1.$ They are then combined to form a bigger drop. The potential of the bigger drop is $V_2.$ Find the ratio $V_2/V_1.$ Ignore the change in density of the fluid on combining the drops.

Figure shows two conducting thin concentric shells of radii $r$ and $3r.$ The outer shell carries charge $q$ and the inner shell is neutral. The amount of charge that flows from the inner shell to the earth after the key $K$ is closed is equal to ${\left(\frac{1}{n}\right)}^{\mathrm{th}}$ of the charge on the outer shell. What is the value of $n?$

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 $\frac{A_1}{A_2}.$

A parallel plate capacitor of capacity $C_0$ is charged to a potential $V_0. E_1$ is the energy stored in the capacitor when the battery is disconnected and the plate separation is doubled, and $E_2$ is the energy stored in the capacitor when the charging battery is kept connected and the separation between the capacitor plates is doubled. Find the ratio $\frac{E_1}{E_2}$