Electrostatics — JEE Main PYQs

Six point charges are kept 60° apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the centre of the circle is ______.
(${ϵ}_0$ is permittivity of free space)

Electric field in a region is given by $\vec{E}=Ax\hat{i}+By\hat{j}$, where $A=10\mathrm{V}/{\mathrm{m}}^2$ and $B=5\mathrm{V}/{\mathrm{m}}^2$. If the electric potential at a point $(10,20)$ is 500 V , then the electric potential at origin is ____ V.

Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :

Five positive charges each having charge $q$ are placed at the vertices of a pentagon as shown in the figure. The electric potential ($V$) and the electric field ($\vec{E}$) at the center O of the pentagon due to these five positive charges are:

Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is :

Two shorts dipoles $(A,B)$, A having charges $\pm 2\mu \mathrm{C}$ and length 1 cm and $B$ having charges $\pm 4\mu \mathrm{C}$ and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point $P$, equi-distant from the …

Two charges $7\mu \mathrm{C}$ and $-2\mu \mathrm{C}$ are placed at $(-9,0,0)\mathrm{cm}$ and $(9,0,0)\mathrm{cm}$ respectively in an external field $E=\frac{\mathrm{A}}{{\mathrm{r}}^2}\hat{\mathrm{r}}$, where …

Three charges $+2\mathrm{q}$, $+3\mathrm{q}$ and $-4\mathrm{q}$ are situated at $(0,-3\mathrm{a})$, $(2\mathrm{a},0)$ and $(-2\mathrm{a},0)$ respectively in the xy plane. The resultant dipole moment about origin is

The electrostatic potential in a charged spherical region of radius $r$ varies as $V=a{r}^3+b$, where $a$ and $b$ are constants. The total charge in the sphere of unit radius is $\alpha \times \pi \mathrm{a}{ϵ}_0$. The value of $\alpha$ is ______.
(permittivity of vacuum …

There are three co-centric conducting spherical shells A, B and C of radii a, b and c respectively. The potential of the spheres A, B and C respectively, are:

Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm. The work done in bringing a charge of 3 nC from infinity to the third corner of the triangle is ____ $\mu \mathrm{J}$. …

A point charge $\mathrm{q}=1\mu \mathrm{C}$ is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge $Q=24\mu \mathrm{C}$, distributed uniformly along its length, as shown in figure. Force between q and wire is ____ N.
(Use …

Identify the correct statements :
A. Electrostatic field lines form closed loops.
B. The electric field lines point radially outward when charge is greater than zero.
C. The Gauss-Law is valid only for inverse-square force.
D. The workdone in moving a charged particle in a static …

Potential energy ($V$) versus distance ($x$) is given by the graph, Rank various regions as per the magnitudes of the force (F) acting on a particle from high to low.

If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is ______ m.
(Atomic number of gold $=79$ and $\frac{1}{4\pi {ϵ}_0}=9\times 10^9$ in SI units)

A point charge of $10^{-8}\mathrm{C}$ is placed at origin. The work done in moving a point charge $2\mu \mathrm{C}$ from point $\mathrm{A}(4,4,2)\mathrm{m}$ to $\mathrm{B}(2,2,1)\mathrm{m}$ is ______ J.
($\frac{1}{4\pi {ϵ}_0}=9\times 10^9$ in SI units)

Two metal plates (A, B) are kept horizontally with separation of $\left(\frac{12}{\pi }\right)\mathrm{cm}$, with plate A on the top. An atomizer jet sprays oil (density $1.5\mathrm{g}/{\mathrm{cm}}^3$) droplets of radius 1 mm horizontally. All oil droplets carry a charge 5 nC …

Two point charges $8\mu \mathrm{C}$ and $-2\mu \mathrm{C}$ are located at $\mathrm{x}=2\mathrm{cm}$ and $\mathrm{x}=4\mathrm{cm}$, respectively on the x-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at th …

Given below are two statements: one is labelled as
Assertion A and the other is labelled as Reason R
Assertion A : In electrostatics, a conductor does not store any net charge inside.
Reason R: Inside the capacitor (with no dielectric medium), the free charge carriers, if placed …

A thin half ring of radius 35 cm is uniformly charged with a total charge of Q coulomb. If the magnitude of the electric field at centre of the half ring is $100\mathrm{V}/\mathrm{m}$, then the value of Q is $\_\_\_\_$ nC.
( …

A three coulomb charge moves from the point $(0,-2,-5)$ to the point $(5,1,2)$ in an electric field expressed as $\overrightarrow{\mathrm{E}}=2x\hat{\mathrm{i}}+3{\mathrm{y}}^2\hat{\mathrm{j}}+4\hat{\mathrm{k}}\mathrm{N}/\mathrm{C}$. The work done in moving the charge is …

The electric potential as a function of $x,y$ is given by $V=5(x^2-y^2)$ V. The electric field at a point $(2,3)$ m is ______ V/m.

Two point charges ${\mathrm{q}}_1=3\mu \mathrm{C}$ and ${\mathrm{q}}_2=-4\mu \mathrm{C}$ are placed at points $(2\hat{i}+3\hat{j}+3\hat{k})$ and $(\hat{i}+\hat{j}+\hat{k})$ respectively. Force on charge ${\mathrm{q}}_2$ is ______ N.
(Take …

Two charged conducting spheres ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ spheres are ${\mathrm{E}}_{\mathrm{S}1}$ and …

Two short electric dipoles A and B having dipole moment $p_1$ and $p_2$ respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point x is making an angle of $60^{\circ }$ with the line joining points O and x. Th …

A line charge of length $\frac{{}^{\prime }{\mathrm{a}}^{\prime }}{2}$ is kept at the center of an edge BC of a cube ABCDEFGH having edge length 'a' as shown in the figure. If the density of line is $\lambda \mathrm{C}$ per unit length, then the total electric flux through all the faces of the cube wi …

An electron is made to enters symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the field region with a horizontal component of velocity $10^6\mathrm{m}/\mathrm{s}$. If the magnitude of the …

For a short dipole placed at origin O , the dipole moment P is along x -axis, as shown in the figure. If the electric potential and electric field at A are ${\mathrm{V}}_0$ and ${\mathrm{E}}_0$, respectively, then the correct combination of the electric potential and electric fie …

A point particle of charge Q is located at P along the axis of an electric dipole 1 at a distance r as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r . The dipoles are made of opposite charge q separated by a distanc …

The electric flux is $\varphi =\alpha \sigma +\beta \lambda$
where $\lambda$ and $\sigma$ are linear and surface charge density, respectively, $\left(\frac{\alpha }{\beta }\right)$ represents

A positive ion A and a negative ion B have charges $6.67\times 10^{-19}\mathrm{C}$ and $9.6\times 10^{-10}\mathrm{C}$, and masses $19.2\times 10^{-27}\mathrm{kg}$ and $9\times 10^{-27}\mathrm{kg}$ respectively. At an instant, the ions are separated by a certain distan …

Two charges $7\mu \mathrm{c}$ and $-4\mu \mathrm{c}$ are placed at $(-7\mathrm{cm}$, 0 , 0 ) and ( $7\mathrm{cm},0,0$ ) respectively. Given, ${ϵ}_0=8.85\times 10^{-12}{\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}$, the electrostatic potential energy of the char …

Two point charges $-4\mu \mathrm{c}$ and $4\mu \mathrm{c}$, constituting an electric dipole, are placed at $(-9,0,0)\mathrm{cm}$ and $(9,0,0)\mathrm{cm}$ in a uniform electric field of strength $10^4{\mathrm{NC}}^{-1}$. The work done on the dipole in rotating it from the equ …

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density ${\sigma }_0$. Choose the correct option from the following. …

A point charge causes an electric flux of $-2\times 10^4{\mathrm{Nm}}^2{\mathrm{C}}^{-1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is :

(Given …

Match List-I with List-II.

(A) Electric field inside (distance $\mathrm{r}>0$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$, and radius R .
(B) Electric field at distance $\mathrm{r}>0$ from a uniformly charged infinite plane sheet with …

An electric dipole of dipole moment $6\times 10^{-6}\mathrm{Cm}$ is placed in uniform electric field of magnitude $10^6\mathrm{V}/\mathrm{m}$. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole momen …

Three infinitely long wires with linear charge density $\lambda$ are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface ?

In the first configuration (1) as shown in the figure, four identical charges ( ${\mathrm{q}}_0$ ) are kept at the corners $\mathrm{A},\mathrm{B},\mathrm{C}$ and D of square of side length ' a '. In the second configuration (2), the same charges are shifted to mid points …

A small uncharged conducting sphere is placed in contact with an identical sphere but having $4\times 10^{-8}$ C charge and then removed to a distance such that the force of repulsion between them is $9\times 10^{-3}\mathrm{N}$. The distance between them is (Take …

A square loop of sides $\mathrm{a}=1\mathrm{m}$ is held normally in front of a point charge $\mathrm{q}=1\mathrm{C}$. The flux of the electric field through the shaded region is $\frac{5}{\mathrm{p}}\times \frac{1}{{\epsilon }_0}\frac{{\mathrm{Nm}}^2}{\mathrm{C}}$, where t …

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field.
Reason (R) : In absence of …

Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is V. The potential difference between the points A and B (shown in the figure) is :

Consider a circular loop that is uniformly charged and has a radius $\mathrm{a}\sqrt{2}$. Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin :

The electrostatic potential on the surface of uniformly charged spherical shell of radius $\mathrm{R}=10\mathrm{cm}$ is 120 V . The potential at the centre of shell, at a distance $\mathrm{r}=5\mathrm{cm}$ from centre, and at a distance $\mathrm{r}=15\mathrm{cm}$ from the c …

Two infinite identical charged sheets and a charged spherical body of charge density '$\rho$' are arranged as shown in figure. Then the correct relation between the electrical fields at A, B, C and D points is :

Two small spherical balls of mass 10 g each with charges $-2\mu \text{C}$ and $2\mu \text{C}$, are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of …

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

Assertion (A) : The outer body of an air craft is made of metal which protects persons sitting inside from lightning-strikes.
Reason (R) : The electric field inside the cavi …

A dipole with two electric charges of $2\mu \mathrm{C}$ magnitude each, with separation distance $0.5\mu \mathrm{m}$, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference …

The electric field in a region is given by $\vec{E}=(2\hat{i}+4\hat{j}+6\hat{k})\times 10^3\mathrm{N}/\mathrm{C}$. The flux of the field through a rectangular surface parallel to $\mathrm{x}-\mathrm{z}$ plane is $6.0{\mathrm{Nm}}^2{\mathrm{C}}^{-1}$. The area of t …