Electrostatics — JEE Main PYQs

512 identical drops of mercury are charged to a potential of 2 V each. The drops are joined to form a single drop. The potential of this drop is ____ V.

The electric field in a region is given by $\vec{E}=\left(\frac{3}{5}{E}_0\hat{i}+\frac{4}{5}{E}_0\hat{j}\right)\frac{N}{C}$. The ratio of flux of reported field through the rectangular surface of area $0.2m^2$ (parallel to $y-z$ plane) to that of the surface of are …

An electric dipole is placed on $x$ - axis in proximity to a line charge of linear density $3.0\times 10^{-6}\mathrm{C}/\mathrm{m}$. Line charge is placed on z -axis and positive and negative charge of dipole is at a distance of 10 mm and 12 mm from the origin respectively. I …

The total charge enclosed in an incremental volume of $2\times 10^{-9}{\mathrm{m}}^3$ located at the origin is ______ nC, if electric flux density of its field is found as …

Find the electric field at point $P$ (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length $L$ carrying a charge $Q$. The distance of the point $P$ from the centre of the rod is $a=\frac{\sqrt{3}}{2}L$.

A uniformly charged disc of radius R having surface charge density $\sigma$ is placed in the xy plane with its center at the origin. Find the electric field intensity along the z-axis at a distance Z from origin :-

Given below are two statements :
Statement I : An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.
Statement II: If R is the radius of a solid metallic sphe …

27 similar drops of mercury are maintained at 10 V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ____ times that of a smaller drop.

Choose the incorrect statement :
(a) The electric lines of force entering into a Gaussian surface provide negative flux.
(b) A charge 'q' is placed at the centre of a cube. The flux through all the faces will be the same.
(c) In a uniform electric field net flux through a closed …

Two particles A and B having charges $20\mu C$ and $-5\mu C$ respectively are held fixed with a separation of 5 cm. At what position a third charged particle should be placed so that it does not experience a net electric force?

Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'ℓ'. What is the equilibrium separation when each thread makes a small angle 'θ' with the vertical?

Two ideal electric dipoles A and B, having their dipole moment $p_1$ and $p_2$ respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole $A$, the resultant electric field is making an angle of $37^{\circ }$ with the axi …

What will be the magnitude of electric field at point O as shown in figure? Each side of the figure is $\ell$ and perpendicular to each other?

A cube is placed inside an electric field, $\vec{E}=150y^2\hat{j}$. The side of the cube is 0.5 m and is placed in the field as shown in the given figure. The charge inside the cube is:

Find out the surface charge density at the intersection of point $x=3m$ plane and $x$-axis, in the region of uniform line charge of $8\mathrm{nC}/\mathrm{m}$ lying along the $z$-axis in free space.

An infinite number of point charges, each carrying $1\mu \mathrm{C}$ charge, are placed along y-axis at $\mathrm{y}=1\mathrm{m},2\mathrm{m},4\mathrm{m},8\mathrm{m}$, ______. The total force on a 1 C point charge, placed at the origin is $x\times 10^{3}N$. The …

The electric field in a region is given by $\vec{E}=\frac{2}{5}{E}_0\hat{i}+\frac{3}{5}{E}_0\hat{j}$ with $E_0=4.0\times 10^3\frac{N}{C}$. The flux of this field through a rectangular surface area $0.4{\mathrm{m}}^2$ parallel to the $Y-Z$ plane is ______ …

An oil drop of radius 2 mm with a density $3{\mathrm{gcm}}^{-3}$ is held stationary under a constant electric field $3.55\times 10^5{\mathrm{Vm}}^{-1}$ in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess?

Consider …

Two infinite planes each with uniform surface charge density $+\sigma$ are kept in such a way that the angle between them is $30^{\circ }$. The electric field in the region shown between them is given by:

In finding the electric field using Gauss law the formula $|\vec{E}|=\frac{q_{\text{enc }}}{{\epsilon }_0|A|}$ is applicable. In the formula ${\epsilon }_0$ is permittivity of free space, A is the area of Gaussain surface and ${\mathrm{q}}_{\mathrm{enc}}$ is charge enclosed by …

Three charged particles $\mathrm{A},\mathrm{B}$ and C with charges $-4q,2q$ and $-2q$ are present on the circumference of a circle of radius d . The charged particles A, C and centre O of the circle formed an equilateral triangle as shown in figure. Electric field at O …

Consider two charged metallic spheres $S_1$ and $S_2$ of radii $R_1$ and $R_2$, respectively. The electric fields $E_1$ (on $S_1$) and $E_2$ (on $S_2$) on their surfaces are such that $E_1/E_2=R_1/R_2$. Then the ratio of $V_1$ (on $S_1$)$/V_2$ (on …

An electric field $\vec{E}=4x\hat{i}-(y^2+1)\hat{j}$ N/C passes through the box shown in figure. The flux of the electric field through surfaces ABCD and BCGF are marked as ${\varphi }_I$ and ${\varphi }_{II}$ respectively. The difference between $({\varphi }_I-{\varphi }_{II})$ is (in …

An electric dipole of moment $\vec{p}=(-\hat{i}-3\hat{j}+2\hat{k})\times 10^{-29}\mathrm{cm}$ is at the origin $(0,0,0)$. The electric field due to this dipole at $\vec{r}=+\hat{i}+3\hat{j}+5\hat{k}$ (note that $\vec{r}\cdot \vec{p}=0$ ) is parallel to:

Consider a sphere of radius $R$ which carries a uniform charge density $\rho$. If a sphere of radius $\frac{R}{2}$ is carved out of it, as shown the ratio $\frac{|{\vec{E}}_A|}{|{\vec{E}}_B|}$ of magnitude of electric field ${\vec{E}}_A$ and ${\vec{E}}_B$, r …

Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge $(+q)$ each, while $2,4,6,8,10$ have charge $(-q)$ each. The potential $V$ and the electric field $E$ at th …

Two isolated conducting spheres $S_1$ and $S_2$ of radius $\frac{2}{3}R$ and $\frac{1}{3}R$ have $12\mu \mathrm{C}$ and -3 $\mu \mathrm{C}$ charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after th …

Concentric metallic hollow spheres of radii $R$ and 4R hold charges $Q_1$ and ${\mathrm{Q}}_2$ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference $V(R)-V(4R)$ is:

Two identical electric point dipoles have dipole moments ${\vec{p}}_1=p\hat{i}$ and ${\vec{p}}_2=-p\hat{i}$ and are held on the $x$ axis at distance '$a$' from each other. When released, they move along the $x$-axis with the direction of their dipole moments remaining unchanged …

Consider the force F on a charge ' q ' due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F , if ' q ' is placed at distance r from the centre of the shell?

Charge $Q_1$ and $Q_2$ are at point $A$ and $B$ of a right angle triangle OAB (see figure). The resultant electric field at point O is perpendicular to the hypotenuse, then $\frac{{\mathrm{Q}}_1}{{\mathrm{Q}}_2}$ is proportional to:

A two point charges $4q$ and $-q$ are fixed on the $x$-axis at $x=-\frac{d}{2}$ and $x=\frac{d}{2}$, respectively. If a third point charge ' $q$ ' is taken from the origin to $x=d$ along the semicircle as shown in the figure, the energy of the charge will:

Two charged thin infinite plane sheets of uniform surface charge density ${\sigma }_{+}$ and ${\sigma }_{-}$, where $\left|{\sigma }_{+}\right|>\left|{\sigma }_{-}\right|$, intersect at right angle. Which of the following best represents the electric field lines for this system.

A solid conducting sphere, having a charge Q , is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V . If the shell is now given a charge of -4 Q …

The election field in a region is given by $\vec{E}=(Ax+B)\hat{i}$ where $E$ is in $N{C}^{-1}$ and $x$ in meters. The values of constants are $A=20$ SI unit and $B=10$ SI unit. If the potential at $x=1$ is $V_1$ and that at $x=-5$ is $V_2$ then $V_1-V_2$ is:

A system of three charges are placed as shown in the figure:

If $\mathrm{D}\gg \mathrm{d}$, the potential energy of the system is best given by:

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

The total potential at a point at distance r from their common cen …

Two electric dipoles $\mathrm{A},\mathrm{B}$ with respective dipole moments $\overrightarrow{{\mathrm{d}}_{\mathrm{A}}}=-4$ qai and $\overrightarrow{{\mathrm{d}}_{\mathrm{B}}}=2$ qai are placed on the $x$-axis with a separation R , as shown in the figure. The distance from A at whic …

An electric field of $1000\mathrm{V}/\mathrm{m}$ is applied to an electric dipole at angle of $45^{\circ }$. The value of electric dipole moment is $10^{-29}\mathrm{C}.\mathrm{m}$. What is the potential energy of the electric dipole?

A particle of mass $m$ and charge $q$ is in an electric and magnetic field given by:

The charged particle is shifted from the origin to the point $P(x=1;y=1)$ along a straight path. The magnitude of the total work done i …

Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius $b$, and carries charge $Q$. At its centre is a dipole $\overrightarrow{\mathrm{P}}$ as shown. In this case :

A point dipole $\overrightarrow{\mathrm{p}}=-{\mathrm{p}}_0\hat{\mathrm{x}}$ is kept at the origin. The potential and electric field due to this dipole on the y -axis at a distance d are, respectively : (Take $\mathrm{V}=0$ at infinity)

Three charges $\mathrm{Q},+\mathrm{q}$ and +q are placed at the vertices of a right - angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of $Q$ is:

The give graph shown variation (with distance r from centre) of:

Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure:

There is a uniform spherically symmetric surface charge density at a distance $R_0$ from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed $\mathrm{V}(\mathrm{R}(\mathrm{t}))$ of …

Let a total charge 2 Q be distributed in a sphere of radius R , with the charge density given by $r(r)=kr$, where $r$ is the distance from the centre. Two charges $A$ and $B$, of $-Q$ each, are placed on diametrically opposite points, at equal distance, a , from the centre. If A …

Four point charges $-q,+q,+q$ and $-q$ are placed on $y$ axis at $y=-2d,y=-d,y=+d$ and $\mathrm{y}=+2\mathrm{d}$, respectively. The magnitude of the electric field E at a point on the x -axis at x $=D$, with $D\gg d$, will vary as:

Two point charges $q_1(\sqrt{10}\mu \mathrm{C})$ and $q_2(-25\mu \mathrm{C})$ are placed on the $x$-axis at $x=1\mathrm{m}$ and $x=4\mathrm{m}$ respectively. The electric field (in $\mathrm{V}/\mathrm{m}$) at a point $y=3\mathrm{m}$ on $y$-axis is, …

Charge is distributed within a sphere of radius R with a volume charge density $\rho (r)=\frac{A}{r^2}{e}^{-2r/a}$, where $A$ and a are constants. If $Q$ is the total charge of this charge distribution, the radius R is: