Electrostatics — JEE Main PYQs

If ${ϵ}_0$ denotes the permittivity of free space and ${\Phi }_E$ is the flux of the electric field through the area bounded by the closed surface, then dimension of $\left({ϵ}_0\frac{d{\varphi }_E}{dt}\right)$ are that of:

Two charges $q_1$ and $q_2$ are separated by a distance of 30 cm. A third charge $q_3$ initially at 'C' as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of $q_3$ from C to D is give …

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen.

Reason R : Electrostatic …

Electric charge is transferred to an irregular metallic disk as shown in figure. If ${\sigma }_1,{\sigma }_2,{\sigma }_3$ and ${\sigma }_4$ are charge densities at given points then, choose the correct answer from the options given below:
(A) …

An infinitely long wire has uniform linear charge density $\lambda =2\mathrm{nC}/\mathrm{m}$. The net flux through a Gaussian cube of side length $\sqrt{3}\mathrm{cm}$, if the wire passes through any two corners of the cube, that are maximally displaced from each other, w …

Two metal spheres of radius $R$ and $3R$ have same surface charge density $\sigma$. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes ${\sigma }_1$ and ${\sigma }_2$, respectively. The ratio …

A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to $\mathrm{arc}\mathrm{AB}$ to ' O ' is ' E ' is magnitude. What would be the magnitude of electric field at ' O ' due to …

A small bob of mass 100 mg and charge $+10\mu \mathrm{C}$ is connected to an insulating string of length 1 m. It is brought near to an infinitely long nonconducting sheet of charge density '$\sigma$' as shown in figure. If string subtends an angle of $45^{\circ }$ with the …

Two identical conducting spheres $P$ and $S$ with charge $Q$ on each, repel each other with a force 16 N . A third identical uncharged conducting sphere R is successively brought in contact with the two spheres. The new force of repulsion between P and S is :

A charge q is placed at the center of one of the surface of a cube. The flux linked with the cube is :-

An infinitely long positively charged straight thread has a linear charge density $\lambda {\mathrm{Cm}}^{-1}$. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron …

An infinite plane sheet of charge having uniform surface charge density $+{\sigma }_{\mathrm{s}}\mathrm{C}/{\mathrm{m}}^2$ is placed on $\mathrm{x}-\mathrm{y}$ plane. Another infinitely long line charge having uniform linear charge density …

The vehicles carrying inflammable fluids usually have metallic chains touching the ground :

The electric field at point p due to an electric dipole is E. The electric field at point R on equitorial line will be $\frac{E}{x}$. The value of $x$:

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of:

$\sigma$ is the uniform surface charge density of a thin spherical shell of radius R . The electric field at any point on the surface of the spherical shell is :

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point P is $\frac{\mathrm{x}\sigma }{{ϵ}_0}$. The value of x is ______ (all quantities are measured in SI units).

Two charged conducting spheres of radii a and b are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

An electric field, $\overrightarrow{\mathrm{E}}=\frac{2\hat{\mathrm{i}}+6\hat{\mathrm{j}}+8\hat{\mathrm{k}}}{\sqrt{6}}$ passes through the surface of $4{\mathrm{m}}^2$ area having unit vector $\hat{n}=\left(\frac{2\hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right)$. The electr …

In an alpha particle scattering experiment distance of closest approach for the $\alpha$ particle is $4.5\times 10^{-14}\mathrm{m}$. If target nucleus has atomic number 80, then maximum velocity of $\alpha$-particle is ____ $\times 10^5\mathrm{m}/\mathrm{s}$ a …

If the net electric field at point P along Y axis is zero, then the ratio of $\left|\frac{{\mathrm{q}}_2}{{\mathrm{q}}_3}\right|$ is $\frac{8}{5\sqrt{\mathrm{x}}}$, where $\mathrm{x}=$ ______

At the centre of a half ring of radius $\mathrm{R}=10\mathrm{cm}$ and linear charge density $4\mathrm{nC}{\mathrm{m}}^{-1}$, the potential is $\mathrm{x}\pi \mathrm{V}$. The value of x is ____.

Five charges $+q,+5q,-2q,+3q$ and $-4q$ are situated as shown in the figure. The electric flux due to this configuration through the surface S is :

An electric field $\overrightarrow{\mathrm{E}}=(2x\hat{\mathrm{i}}){\mathrm{NC}}^{-1}$ exists in space. A cube of side 2 m is placed in the space as per figure given below. The electric flux through the cube is ................ ${\mathrm{Nm}}^2/\mathrm{C}$.

Given below are two statements : one is labelled a Assertion (A) and the other is labelled as Reason(R)
Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero.
Reason (R) : Electric lines of forces are always perpendicul …

Two charges of $-4\mu \mathrm{C}$ and $+4\mu \mathrm{C}$ are placed at the points $\mathrm{A}(1,0,4)\mathrm{m}$ and $\mathrm{B}(2,-1,5)\mathrm{m}$ located in an electric field $\overrightarrow{\mathrm{E}}=0.20\hat{\mathrm{i}}\mathrm{V}/\mathrm{cm}$. The magnitud …

The electric potential at the surface of an atomic nucleus ($\mathrm{z}=50$) of radius $9\times 10^{-13}\mathrm{cm}$ is ____ $\times 10^6\mathrm{V}$.

An electric field is given by $(6\hat{\mathrm{i}}+5\hat{\mathrm{j}}+3\hat{\mathrm{k}})\mathrm{N}/\mathrm{C}$.

The electric flux through a surface area $30\hat{\mathrm{i}}{\mathrm{m}}^2$ lying in YZ-plane (in SI unit) is:

An electric charge $10^{-6}\mu \mathrm{C}$ is placed at origin $(0,0)$ m of $\mathrm{X}-\mathrm{Y}$ co-ordinate system. Two points P and $Q$ are situated at $(\sqrt{3},\sqrt{3})$ m and $(\sqrt{6},0)$ m respectively. The potential difference between the points P and …

A thin metallic wire having cross sectional area of $10^{-4}{\mathrm{m}}^2$ is used to make a ring of radius 30 cm. A positive charge of $2\pi \mathrm{C}$ is uniformly distributed over the ring, while another positive charge of 30 pC is kept at the centre of the ring. The …

Two charges of 5Q and -2Q are situated at the points ($3\mathrm{a},0$) and ($-5\mathrm{a},0$) respectively. The electric flux through a sphere of radius '4a' having center at origin is:

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density $+\sigma$. The electron at $\mathrm{t}=0$ is at a distance of 1 m from S and has a speed of $1m/s$. The maximum value of $\sigma$ …

Two charges q and 3 q are separated by a distance '$r$' in air. At a distance x from charge q , the resultant electric field is zero. The value of x is :

${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ are two hollow concentric cubes enclosing charges 2 Q and 3 Q respectively as shown in figure. The ratio of electric flux passing through ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ is :

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is $1.5\mathrm{g}/\mathrm{cc}$, the dielectric constan …

A particle of charge '$-q$' and mass '$m$' moves in a circle of radius '$r$' around an infinitely long line charge of linear density '$+\lambda$'. Then time period will be given as:
(Consider k as Coulomb's constant)

Two identical charged spheres are suspended by string of equal lengths. The string make an angle of $37^{\circ }$ with each other. When suspended in a liquid of density $0.7\mathrm{g}/{\mathrm{cm}}^3$, the angle remains same. If density of material of the sphere is …

The electrostatic potential due to an electric dipole at a distance ' $r$ ' varies as :

Force between two point charges $q_1$ and $q_2$ placed in vacuum at 'r' cm apart is F. Force between them when placed in a medium having dielectric $K=5$ at 'r/5' cm apart will be:

The distance between charges +q and -q is $2l$ and between +2 q and -2 q is $4l$. The electrostatic potential at point P at a distance r from centre O is $-\alpha \left[\frac{ql}{r^2}\right]\times 10^{9}V$, where the value of $\alpha$ is ______. (Use …

Electric potential at a point 'P' due to a point charge of $5\times 10^{-9}\mathrm{C}$ is 50 V. The distance of 'P' from the point charge is:
(Assume, $\frac{1}{4\pi {\epsilon }_0}=9\times 10^{+9}{\mathrm{Nm}}^2{\mathrm{C}}^{-2}$)

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $R$, with distance $r$ from the centre $O$ is represented by:

An electric dipole of dipole moment is $6.0\times 10^{-6}\mathrm{Cm}$ placed in a uniform electric field of $1.5\times 10^3{\mathrm{NC}}^{-1}$ in such a way that dipole moment is along electric field. The work done in rotating dipole by $180^{\circ }$ in this field will …

An electron revolves around an infinite cylindrical wire having uniform linear charge density $2\times 10^{-8}{\mathrm{Cm}}^{-1}$ in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is …

Three concentric spherical metallic shells $\mathrm{X}$, $\mathrm{Y}$ and $\mathrm{Z}$ of radius $\mathrm{a}$, $\mathrm{b}$ and $\mathrm{c}$ respectively $[\mathrm{a}<\mathrm{b}<\mathrm{c}]$ have surface charge densities $\sigma$, $-\sigma$ and $\sigma$, respectively. The shells …

As shown in the figure, a configuration of two equal point charges ($q_0=-2\mu \mathrm{C}$) is placed on an inclined plane. Mass of each point charge is 20 g. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (a …

Given below are two statement: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : If an electric dipole of dipole moment $30\times 10^{-5}\mathrm{Cm}$ is enclosed by a closed surface, the net flux coming out of the surface will be zero.
Reason R …

64 identical drops each charged upto potential of 10 mV are combined to form a bigger dorp. The potential of the bigger drop will be ____ mV .

Two charges each of magnitude 0.01 C and separated by a distance of 0.4 mm constitute an electric dipole. If the dipole is placed in an uniform electric field ' $\overrightarrow{\mathrm{E}}$ ' of 10 dyne/C making $30^0$ angle with $\overrightarrow{\mathrm{E}}$, the magnit …

A thin infinite sheet charge and an infinite line charge of respective charge densities $+\sigma$ and $+\lambda$ are placed parallel at 5 m distance from each other. Points 'P' and 'Q' are at $\frac{3}{\pi }\mathrm{m}$ and $\frac{4}{\pi }\mathrm{m}$ perpendicular distan …