## Important Questions on Electrostatics

EASY

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

A metallic sphere is kept in between two oppositely charged plates. The most appropriate representation of the field lines is

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

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

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

Consider a cube of uniform charge density, $\rho $. The ratio of the electrostatic potential at the center of the cube to that at one of the corners of the cube is,

MEDIUM

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $P$, in the region, is found to vary between the limits $589.0\mathrm{V}$ to $589.8\mathrm{V}$. What is the potential at a point on the sphere whose radius vector makes an angle of $60\xb0$ with the direction of the field?

MEDIUM

When an $\mathrm{\alpha}$ -particle of mass $m$ moving with a undefined velocitybombards on a heavy nucleus of charge $\mathrm{Ze}$, its distance of the closest approach from the nucleus depends on $m$ as:

EASY

An electron with an initial speed of $4.0\times {10}^{6}\mathrm{}\mathrm{m}{\mathrm{s}}^{-1}$ is brought to rest by an electric field. The mass and charge of an electron are $9\times {10}^{-31}\mathrm{kg}$ and $1.6\times {10}^{-19}\mathrm{C}$, respectively. Identify the correct statement.

EASY

An electric field $\overrightarrow{E}=\left(25\widehat{\mathrm{i}}+30\widehat{\mathrm{j}}\right)\mathrm{N}{\mathrm{C}}^{-1}$ exists in a region of space. If the potential at the origin is taken to be zero then the potential at $x=2\mathrm{m}$, $y=2\mathrm{m}$ is:

HARD

Consider a spherical shell of radius $R$ with a total charge $+Q$ uniformly spread on its surface (center of the shell lies at the origin $x=0$ ). Two point charge, $+q\mathrm{a}\mathrm{n}\mathrm{d}-q$ are brought, one after the other, from far away and placed at $x=-\frac{a}{2}\mathrm{a}\mathrm{n}\mathrm{d}x=+\frac{a}{2}\left(a<R\right),$ respectively. Magnitude of the work done in this process is

HARD

Four equal point charges $Q$ each are placed in the $xy$ plane at $\left(0,\text{\hspace{0.17em}}2\right),\left(4,\text{\hspace{0.17em}}2\right),\left(4,\text{\hspace{0.17em}}-2\right)$ and $\left(0,\text{\hspace{0.17em}}-2\right)$ . The work required to put a fifth charge $Q$ at the origin of the coordinate system will be:

MEDIUM

A charge $Q$ is distributed over three concentric spherical shells of radii $a,b,c\left(a<b<c\right)$ such that their surface charge densities are equal to one another.

The total potential at a point at distance $r$ from their common centre, where $r<a,$ would be:

HARD

A point particle of mass $0.5\mathrm{kg}$ is moving along the $X$ -axis under a force described by the potential energy $V$ shown below. It is projected towards the right from the origin with a speed $v$.

What is the minimum value of $v$ for which the particle will escape infinitely far away from the origin?

MEDIUM

Four point charge (with equal magnitude of charge of $5C;$but with different signs) are placed at four corners of a square of side $10\mathrm{m}.$Assuming that the square is centered at the origin and the configuration of the charges are as given in the figure, the potential and the magnitude of electric field at the origin, respectively are

[Note$\left.k=\frac{1}{4\pi {\epsilon}_{0}}\right]$

EASY

The diagrams below show regions of equipotential.

A positive charge is moved from $A$ to $B$ in each diagram.

MEDIUM

Two equal charges of magnitude $Q$ each are placed at a distance $d$ apart. Their electrostatic energy is $E.A.$ third charge $-\frac{Q}{2}$ is brought midway betweenthese two charges. The electrostatic energy of the system is now?

MEDIUM

A certain p-n junction having a depletion region of width $20\mathrm{\mu m},$ was found to have a breakdown voltage of $100\mathrm{V}$. If the width of the depletion region is reduced to $1\mathrm{\mu m}$ during its production, then it can be used as a zener diode for voltage regulation of:

EASY

The electric potential at a point $\left(x,y\right)$ in the $x$-$y$ plane is given by

$V=-Kxy$

The electric field intensity at a distance $r$ from the origin varies as

HARD

Some equipotential surfaces are shown. The electric field at any point is

EASY

If potential(in $\mathrm{volts}$) in a region is expressed as$V\left(x,y,z\right)=6xy-y+2yz$, the electric field(in$\mathrm{N}{\mathrm{C}}^{-1}$) at point$\left(1,1,0\right)$is

MEDIUM

Four point charges $-Q,-q,2q$ and $2Q$ are placed, one at each corner of the square. The relation between $Q$ and $q$ for which the potential at the centre of the square is zero is

EASY

$N$ number of charges, $+Q$ each, are placed maintaining equal distance on the circumference of a circle of radius $R.$ The net electrostatic potential at the centre of the circle is