Electrostatics Questions

A charged oil drop is suspended in a uniform field of $3\times 10^4\text{V/m}$ so that it neither falls nor rises. The charge on the drop will be: (Take mass of the drop $=9.9\times 10^{-15}\text{kg}$ and $g=10{\text{m/s}}^2$)

Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium, the value of $q$ is:

A charged particle $q$ is shot towards another charged particle $Q$ which is fixed. With a speed $v$, it approaches $Q$ up to a closest distance $r$ and then returns. If $q$ were given a speed $2v$, the closest distance of approach would be:

Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges $q$ repel each other with a force $F$ when kept apart at some distance. A third spherical conductor having same radius as that of $B$ but uncharged is brought in contact with $B$, then brought in contact with $C$ and finally removed away from both. The new force of repulsion between $B$ and $C$ is:

A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be:

An electric charge $10^{-3}\mu \text{C}$ is placed at the origin $(0,0)$ of $X-Y$ co-ordinate system. Two points $A$ and $B$ are situated at $(\sqrt{2},\sqrt{2})$ and $(2,0)$ respectively. The potential difference between the points $A$ and $B$ will be:

Two spherical conductors $A$ and $B$ of radii $1\text{mm}$ and $2\text{mm}$ are separated by a distance of $5\text{cm}$ and are uniformly charged. If the spheres are connected by a conducting wire, then in equilibrium, the ratio of the magnitude of the electric fields at the surface of spheres $A$ and $B$ is:

Two infinitely large insulating plates are uniformly charged such that the potential difference between them is $V_2-V_1=20\text{V}$. The plates are separated by $d=0.1\text{m}$. An electron is released from rest on the inner surface of plate 1. What is its speed when it hits plate 2? ($e=1.6\times 10^{-19}\text{C}$, $m_e=9.11\times 10^{-31}\text{kg}$)

An electric dipole is placed at an angle of $30^{\circ }$ to a non-uniform electric field. The dipole will experience:

Charges $+q,+q,-q,-q$ are placed at the vertices $A,B,C,D$ of a square respectively. Let $\vec{E}$ be the electric field and $V$ the potential at the centre. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ respectively, then:

The potential at a point $x$ (measured in $\mu \text{m}$) due to some charges situated on the $x$ -axis is given by $V(x)=20/(x^2-4)$ Volts. The electric field $E$ at $x=4\mu \text{m}$ is given by:

A parallel plate condenser with a dielectric of dielectric constant $K$ between the plates has a capacity $C$ and is charged to a potential $V$ volts. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is:

If $g_E$ and $g_m$ are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio of electronic charge on the moon to electronic charge on the earth to be:

A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then the $Q/q$ equals:

Two points $P$ and $Q$ are maintained at the potentials of $10\text{V}$ and $-4\text{V}$ respectively. The work done in moving $100$ electrons from $P$ to $Q$ is:

Statement 1: When a charge $q$ is taken from the centre to the surface of an insulating solid sphere of radius $R$ and uniform charge density $\rho$, its potential energy changes by $\frac{q\rho R^2}{3{ϵ}_0}$.Statement 2: The electric field at a distance $r(r<R)$ from the centre of the sphere is $\frac{\rho r}{3{ϵ}_0}$.

Let $\rho (r)=\frac{Qr}{\pi R^4}$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point '$p$ ' inside the sphere at distance $r_1$ from the centre of the sphere, the magnitude of electric field is:

A thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net electric field $\vec{E}$ at the centre $O$ is:

Let there be a spherically symmetric charge distribution with charge density varying as $\rho (r)={\rho }_0(\frac{5}{4}-\frac{r}{R})$ up to $r=R$, and $\rho (r)=0$ for $r>R$. The electric field at a distance $r(r<R)$ from the origin is given by:

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ }$ with each other. When suspended in a liquid of density $0.8{\text{g cm}}^{-3}$, the angle remains the same. If density of the material of the sphere is $16{\text{g cm}}^{-3}$, the dielectric constant of the liquid is:

Two identical charged spheres suspended from a common point by two massless strings of length $l$ are initially a distance $d$ ($d\ll l$) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity $v$. Then as a function of distance $x$ between them:

The electrostatic potential inside a charged spherical ball is given by $\varphi =a{r}^2+b$ where $r$ is the distance from the centre; $a,b$ are constants. Then the charge density inside ball is:

In a uniformly charged sphere of total charge $Q$ and radius $R$, the electric field $E$ is plotted as a function of distance $r$ from the centre. The graph which would correspond to the above will be:

A charged ball $B$ hangs from a silk thread $S$ which makes an angle $\theta$ with a large charged conducting sheet $P$, as shown in the figure. The surface charge density $\sigma$ of the sheet is proportional to:

This question contains Statement-1 and Statement-2. Of the four choices given after the statements,
choose the one that best describes the two statements.
Statement – 1: For a charged particle moving from point P to point Q, the net work done by an
electrostatic field on the particle is independent of the path connecting point P to point Q.
Statement-2: The net work done by a conservative force on an object moving along a closed loop is
zero

A thin spherical shell of radius $R$ has charge $Q$ spread uniformly. Which graph represents the electric field $E(r)$ for $0\le r<\infty$?

A parallel plate capacitor with air between the plates has a capacitance of $9\text{pF}$. The separation between its plates is ‘$d$ ’. The space between the plates is now filled with two dielectrics. One has $k_1=3$ and thickness $d/3$ while the other has $k_2=6$ and thickness $2d/3$. Capacitance of the capacitor is now:

A thin spherical conducting shell of radius $R$ has a charge $q$. Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at a point $P$ at a distance $R/2$ from the centre of the shell is:

A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor:

The work done in placing a charge of $8\times 10^{-18}$ coulomb on a condenser of capacity $100$ micro-farad is:

Three charges $-q_1$, $+q_2$ and $-q_3$ are placed as shown in the figure. ($-q_1$ at origin, $+q_2$ at $(b,0)$, $-q_3$ at $(a\cos \theta ,a\sin \theta )$). The $x$ -component of the force on $-q_1$ is proportional to:

If the electric flux entering and leaving an enclosed surface respectively is ${\varphi }_1$ and ${\varphi }_2$, the electric charge inside the surface will be:

Two thin wire rings each having a radius $R$ are placed at a distance $d$ apart with their axes coinciding. The charges on the two rings are $+q$ and $-q$. The potential difference between the centres of the two rings is:

Two point charges $+8q$ and $-2q$ are located at $x=0$ and $x=L$ respectively. The location of a point on the x-axis at which the net electric field due to these two point charges is zero is: