Electrostatics — JEE Main PYQs

A $10\mu \mathrm{C}$ charge is divided into two parts and placed at 1 cm distance so that the repulsive force between them is maximum. The charges of the two parts are :

Three point charges $\mathrm{q},-2\mathrm{q}$ and 2 q are placed on x -axis at a distance $x=0,x=\frac{3}{4}R$ and $x=R$ respectively from origin as shown. If $\mathrm{q}=2\times 10^{-6}\mathrm{C}$ and $\mathrm{R}=2\mathrm{cm}$, the magnitude of net force experienced by th …

The electric field due to a short electric dipole at a large distance (r) from center of dipole on the equatorial plane varies with distance as :

For a uniformly charged thin spherical shell, the electric potential (V) radially away from the center (O) of shell can be graphically represented as

A capacitor of capacitance C is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is:

Let $\sigma$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region $E_{\mathrm{I}}$, $E_{\mathrm{II}}$ and $E_{\mathrm{III}}$ are:

Two equal positive point charges are separated by a distance $2a$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $q_0$ becomes maximum is $\frac{a}{\sqrt{x}}$. …

If two charges ${\mathrm{q}}_1$ and ${\mathrm{q}}_2$ are separated with distance ' $d$ ' and placed in a medium of dielectric constant K . What will be the equivalent distance between charges in air for the same electrostatic force ?

The electric potential at the centre of two concentric half rings of radii $R_1$ and $R_2$, having same linear charge density $\lambda$ is

Match List I with List II :

List I:
A. Gauss's Law in Electrostatics
B. Faraday's Law
C. Gauss's Law in Magnetism
D. Ampere-Maxwell Law

List II:
I. $\oint \vec{E}.d\vec{l}=-\frac{d{\varphi }_B}{dt}$
II. …

A point charge of $10\mu \mathrm{C}$ is placed at the origin. At what location on the X -axis should a point charge of $40\mu \mathrm{C}$ be placed so that the net electric field is zero at $\mathrm{x}=2\mathrm{cm}$ on the X -axis?

In a cuboid of dimension $2\mathrm{L}\times 2\mathrm{L}\times \mathrm{L}$, a charge q is placed at the centre of the surface ' $S$ ' having area of $4{\mathrm{L}}^2$. The flux through the opposite surface to ' S ' is given by

A point charge $q_1=4q_0$ is placed at origin. Another point charge $q_2=-q_0$ is placed at $x=12\mathrm{cm}$. Charge of proton is $q_0$. The proton is placed on x-axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the …

A point charge $2\times 10^{-2}\mathrm{C}$ is moved from P to S in a uniform electric field of $30{\mathrm{NC}}^{-1}$ directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work done by electric field will be

For a charged spherical ball, electrostatic potential inside the ball varies with r as $V=2a{r}^2+b$.
Here, a and b are constant and r is the distance from the center. The volume charge density inside the ball is $-\lambda a\epsilon$. The value of $\lambda$ is ______. …

As shown in the figure, a point charge Q is placed at the centre of conducting spherical shell of inner radius $a$ and outer radius $b$. The electric field due to charge Q in three different regions I, II and III is given by : (I : $r<a$, II : $a<r<b$, III : $r>b$)

As shown in figure, a cuboid lies in a region with electric field $E=2x^2\hat{i}-4y\hat{j}+6\hat{k}$ N/C. The magnitude of charge within the cuboid is $n{ϵ}_0$ C. The value of n is ______ (if dimension of cuboid is $1\times 2\times 3$ m³)

Two isolated metallic solid spheres of radii $R$ and 2R are charged such that both have same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is ${\sigma }^{\prime }$. The ratio …

Electric field in a certain region is given by $\vec{E}=\left(\frac{A}{x^2}\hat{i}+\frac{B}{y^3}\hat{j}\right)$. The SI unit of $A$ and $B$ are :

Which of the following correctly represents the variation of electric potential (V) of a charged spherical conductor of radius (R) with radial distance $(\mathrm{r})$ from the centre?

Expression for an electric field is given by $\overrightarrow{\mathrm{E}}=4000{\mathrm{x}}^2\hat{\mathrm{i}}\frac{\mathrm{V}}{\mathrm{m}}$. The electric flux through the cube of side 20 cm when placed in electric field (as shown in the figure) is $\_\_\_\_$ V cm.

Considering a group of positive charges, which of the following statements is correct?

A cubical volume is bounded by the surfaces $x=0,x=a,y=0,y=a,z=0,z=a$. The electric field in the region is given by $\vec{E}=E_{0}x\hat{i}$, where $E_0=4\times 10^4\mathrm{N}{\mathrm{C}}^{-1}{\mathrm{m}}^{-1}$. If $a=2\mathrm{cm}$, the charge contained in the cubical v …

Two identical metallic spheres A and B when placed at certain distance in air repel each other with a force of F. Another identical uncharged sphere C is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres A and B. The force ex …

An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particals will be :

Two electric dipoles of dipole moments $1.2\times 10^{-30}$ C m and $2.4\times 10^{-30}$ C m are placed in two different uniform electric fields of strengths $5\times 10^4$ NC${}^{-1}$ and $15\times 10^4$ NC${}^{-1}$ respectively. The ratio of maximum torque experienced by th …

A long cylindrical volume contains a uniformly distributed charge of density $\rho {\mathrm{Cm}}^{-3}$. The electric field inside the cylindrical volume at a distance $\mathrm{x}=\frac{2{\epsilon }_0}{\rho }\mathrm{m}$ from its axis is $\_\_\_\_$ ${\mathrm{Vm}}^{-1}$

The volume charge density of a sphere of radius 6 m is $2\mu \mathrm{C}{\mathrm{cm}}^{-3}$. The number of lines of force per unit surface area coming out from the surface of the sphere is $\_\_\_\_$ $\times 10^{10}{\mathrm{NC}}^{-1}$.
[Given : Permittivity of vacuum …

Two uniformly charged spherical conductors A and B of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere A and …

Three point charges of magnitude $5\mu \mathrm{C}$, $0.16\mu \mathrm{C}$ and $0.3\mu \mathrm{C}$ are located at the vertices $\mathrm{A}$, $\mathrm{B}$, $\mathrm{C}$ of a right angled triangle whose sides are $\mathrm{AB}=3\mathrm{cm}$, $\mathrm{BC}=3\sqrt{2}\mathrm{cm}$ a …

A charge of $4\mu \mathrm{C}$ is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be:

Two point charges $A$ and $B$ of magnitude $+8\times 10^{-6}\mathrm{C}$ and $-8\times 10^{-6}\mathrm{C}$ respectively are placed at a distance d apart. The electric field at the middle point O between the charges is $6.4\times 10^4{\mathrm{NC}}^{-1}$. The distance …

Three identical charged balls each of charge 2 C are suspended from a common point P by silk threads of 2 m each (as shown in figure). They form an equilateral triangle of side 1 m .

The ratio of net force on a charged ball to the force between any two charged balls will be :

Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from mid-point on the perpendicular bisector. The value of x at which charge q will experience the maximum Coulomb's force is :

If the electric potential at any point $(x,y,z)m$ in space is given by $\mathrm{V}=3{\mathrm{x}}^2$ volt. The electric field at the point $(1,0,3)\mathrm{m}$ will be :

Sixty four conducting drops each of radius 0.02 m and each carrying a charge of $5\mu \mathrm{C}$ are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be :

Assertion (A) : Non-polar amterials do not have my permanent dipole moment.

Reason (R) : When an non-polar material is placed in a electric field. the centre of the positive charge distribution of it's individual atom or molecule coinsides with the centre of the negative charge …

A spherically symmetric charge distribution is considered with charge density varying as
$\rho (r)=\{\begin{array}{ll}{\rho }_0\left(\frac{3}{4}-\frac{r}{R}\right)& \text{ for }r\le R\\ \text{ Zero }& \text{ for }r>R\end{array}$
Where, $\mathrm{r}(\mathrm{r}<\mathrm{R})$ is th …

Given below are two statements.
Statement I: Electric potential is constant within and at the surface of each conductor.
Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.
In the light of the above state …

A vertical electric field of magnitude $4.9\times 10^5\mathrm{N}/\mathrm{C}$ just prevents a water droplet of a mass 0.1 g from falling. The value of charge on the droplet will be : (Given $\mathrm{g}=9.8\mathrm{m}/{\mathrm{s}}^2$ )

Two identical charged particles each having a mass 10 g and charge $2.0\times 10^{-7}$ C are placed on a horizontal table with a separation of L between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is 0.25 , …

A long cylindrical volume contains a uniformly distributed charge of density $\rho$. The radius of cylindrical volume is $R$. A charge particle (q) revolves around the cylinder in a circular path. The kinetic of the particle is :

27 identical drops are charged at 22 V each. They combine to form a bigger drop. The potential of the bigger drop will be $\_\_\_\_$ V.

In the figure, a very large plane sheet of positive charge is shown. ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ are two points at distance $l$ and $2l$ from the charge distribution. If $\sigma$ is the surface charge density, then the magnitude of electric fields …

A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius $b$ as shown in figure. The approximate variation electric field $\vec{E}$ as a function of distince $r$ from centre $O$ is given by:

A cube of side '$a$' has point charges $+Q$ located at each of its vertices except at the origin where the charge is -Q. The electric field at the centre of cube is:

The two thin coaxial rings, each of radius ' $a$ ' and having charges $+Q$ and $-Q$ respectively are separated by a distance of ' $s$ '. The potential difference between the centres of the two rings is:

A certain charge $Q$ is divided into parts $q$ and $(Q-q)$. How should the charges $Q$ and $q$ be divided so that q and $(Q-q)$ placed at a certain distance apart experience maximum electrostatic repulsion ?

A point charge of $+12\mu \mathrm{C}$ is at a distance 6 cm vertically above the centre of a squared of side 12 cm as shown in figure. The magnitude of the electric flux through the square will be........... $\times 10^3{\mathrm{Nm}}^2/\mathrm{C}$.

Figure shows a rod AB, which is bent in a $120^{\circ }$ circular arc of radius $R$. A charge ($-Q$) is uniformly distributed over rod $AB$. What is the electric field $\vec{E}$ at the centre of curvature O ?