JEE Electrostatics PYQs with Solutions PDF, Download Now

Consider two identical metallic spheres of radius R each having charge Q and mass m. Their centers have an initial separation of 4R. Both the spheres are given an initial speed of u towards each other. The minimum value of u, so that they can just touch each other is :
(Take $$k= \frac{1}{4\pi \epsilon_{0}}$$ and assume $$kQ^{2}$$ > $$Gm^{2}$$ where G is the Gravitational constant)

A point charge of $$10^{-8}$$ is placed at origin. The work done in moving a point charge $$2 \mu C$$ from point A(4, 4, 2) m to B(2, 2, 1) m is _____J $$\left(\frac{1}{4\pi\epsilon _{0}}=9\times10^{9} \text{in SI units}\right)$$

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 $$(\overrightarrow{E})$$ 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 :

Six point charges are kept $$60^{o}$$ apart from each other on the circumference of a
circle of radius $$R$$ as shown in figure . The net electric field at the center of the circle is______.
( $$\epsilon_{o}$$ is permittivity of free space)

A simple pendulum has a bob with mass $$m$$ and charge $$q$$. The pendulum string has negligible mass. When a uniform and horizontal electric field it is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is ______.
($$g$$: acceleration due to gravity)

Three charges+ 2q, +3q and -4q are situated at (0, -3a), (2a, 0) and (-2a, 0) respectively in the x y plane. The resultant dipole moment about origin is ___ .

A point charge q = l $$\mu C$$ is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge Q = 24 $$\mu C$$, distributed uniformly along its length, as shown in figure. Force between q and wire is __ N.
(Use: $$\frac{1}{4\pi\epsilon_{0}}=9 \times10^{9} N.m^{2}/C^{2}$$)

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 of3 nC from infinity to the third corner of the triangle is __ $$\mu J$$
$$\frac{1}{4\pi \in_{\circ}}=9\times 10^{9}N.m^{2}/C^{2}$$

Two shorts dipoles $$(A, B)$$, $$A$$ having charges $$\pm 2\mu C$$ and length 1 cm and $$B$$ having charges $$\pm 4\mu C$$ 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 centres of both dipoles is ____ N/ C.

Identify the correct statements :
A. Electrostatic field lines form closed loops .
B. The eleclric 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 eleclric field around a closed path is zero.
E. The motion of a particle under Coulomb's force must take place in a plane.
Choose the correct answer from the options given below:

A line charge of length $$\frac{'a'}{2}$$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 charge is $$\lambda C$$ per unit length, then the total electric flux through

all the faces of the cube will be . (Take, $$\epsilon _o$$ as the free space permittivity)

Two point charges $$-4\mu c$$ and $$4\mu c$$, constituting an electric dipole, are placed at (−9, 0, 0)cm and (9, 0, 0)cm in a uniform electric field of strength $$10^{4}NC^{-1}$$. The work done on the dipole in rotating it from the equilibrium through $$180^{\circ}$$ is :

$$ \text{A square loop of sides } a=1\,m \text{ is held normally in front of a point charge } q=1\,C. \text{ The flux of the electric field through the shaded region is } \frac{5}{p}\times\frac{1}{\varepsilon_0}\,Nm^2C^{-1}, \text{ where the value of } p \text{ is } \underline{\hspace{1cm}}. $$

A small uncharged conducting sphere is placed in contact with an identical sphere but having $$4\times10^{-8} C$$ charge and then removed to a distance such that the force of repulsion between them is $$9\times10^{-3} N$$. The distance between them is $$ \text{ (Take } \frac{1}{4\pi \epsilon_o} \text{ as }9\times10^{9} \text{ in SI units)}$$

A particle of mass 'm' and charge 'q'is fastened to one end 'A' of a massless string having equilibrium length l, whose other end is fixed at point 'O'. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the x -axis is

An electric dipole of mass m, charge q, and length $$l$$ is placed in a uniform electric field $$\overrightarrow{E} = E_{\circ}\hat{i}$$. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:

Choose the correct answer from the options given below :

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 distance 2a. For the charge particle at P not to experience any net

force, which of the following correctly describes the situation?

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

A point charge causes an electric flux of $$-2 \times 10^{4}\,\text{N m}^2 \text{C}^{-1}$$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is : (Given $$\varepsilon_0 = 8.85 \times 10^{-12}\,\text{C}^2 \text{N}^{-1} \text{m}^{-2}$$ )

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.

An infinitely long positively charged straight thread has a linear charge density $$\lambda\ Cm^{-1}$$. 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 as a function of radius of circular path from the wire is:

An infinite plane sheet of charge having uniform surface charge density $$+\sigma_s\ C/m^2$$ is placed on x−y plane. Another infinitely long line charge having uniform linear charge density $$+\lambda_e\ C/m$$ is placed at z = 4 m plane and parallel to y-axis. If the magnitude values $$|\sigma_s| = 2|\lambda_e|$$, then at point (0, 0, 2), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $$\pi\sqrt{n} : 1$$. The value of n is _____.

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

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 $$1.5$$ g/cc, the dielectric constant of water will be ______. (Take density of water $$= 1$$ g/cc)

The current in a conductor is expressed as $$I = 3t^2 + 4t^3$$, where $$I$$ is in Ampere and $$t$$ is in second. The amount of electric charge that flows through a section of the conductor during $$t = 1$$ s to $$t = 2$$ s is ____________ C.

$$C_1$$ and $$C_2$$ are two hollow concentric cubes enclosing charges $$2Q$$ and $$3Q$$ respectively as shown in figure. The ratio of electric flux passing through $$C_1$$ and $$C_2$$ is

Suppose a uniformly charged wall provides a uniform electric field of $$2 \times 10^4 \text{ N C}^{-1}$$ normally. A charged particle of mass 2 g being suspended through a silk thread of length 20 cm and remain stayed at a distance of 10 cm from the wall. Then the charge on the particle will be $$\frac{1}{\sqrt{x}} \mu C$$ where $$x$$ = ______ [use $$g = 10 \text{ m s}^{-2}$$]

A thin metallic wire having cross sectional area of $$10^{-4} \text{ m}^2$$ is used to make a ring of radius $$30$$ cm. A positive charge of $$2\pi$$ C is uniformly distributed over the ring, while another positive charge of $$30$$ pC is kept at the centre of the ring. The tension in the ring is _______ N; provided that the ring does not get deformed (neglect the influence of gravity). (Given, $$\frac{1}{4\pi\epsilon_0} = 9 \times 10^9$$ SI units)

Two charges of $$-4 \mu$$C and $$+4 \mu$$C are placed at the points $$A(1, 0, 4)$$ m and $$B(2, -1, 5)$$ m located in an electric field $$\vec{E} = 0.20\hat{i}$$ V cm$$^{-1}$$. The magnitude of the torque acting on the dipole is $$8\sqrt{\alpha} \times 10^{-5}$$ N m, where $$\alpha$$ = _____.

Two charges of $$5Q$$ and $$-2Q$$ are situated at the points $$(3a, 0)$$ and $$(-5a, 0)$$ respectively. The electric flux through a sphere of radius $$4a$$ having centre 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 $$t = 0$$ is at a distance of $$1$$ m from $$S$$ and has a speed of $$1$$ m s$$^{-1}$$. The maximum value of $$\sigma$$, if the electron strikes $$S$$ at $$t = 1$$ s is $$\alpha \left[\frac{m\varepsilon_0}{e}\right] \frac{C}{m^2}$$. The value of $$\alpha$$ is _______.

An electric field is given by $$\left(6\hat{i} + 5\hat{j} + 3\hat{k}\right)$$ N C$$^{-1}$$. The electric flux through a surface area $$30\hat{i}$$ m$$^2$$ lying in YZ-plane (in SI unit) is:

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

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 strings of equal lengths. The string make an angle of $$37°$$ with each other. When suspended in a liquid of density $$0.7$$ g cm$$^{-3}$$, the angle remains same. If density of material of the sphere is $$1.4$$ g cm$$^{-3}$$, the dielectric constant of the liquid is _____ ($$\tan 37° = \frac{3}{4}$$)

Two charges $$q$$ and $$3q$$ 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 :

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 $$\frac{r}{5}$$ cm apart will be:

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

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 :

Two identical conducting spheres $$P$$ and $$S$$ with charge $$Q$$ on each, repel each other with a force $$16 \text{ N}$$. 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 :

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:

If the net electric field at point P along Y axis is zero, then the ratio of $$\left|\frac{q_2}{q_3}\right|$$ is $$\frac{8}{5\sqrt{x}}$$, where $$x =$$ _____

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 $$\vec{E} = (2x\hat{i}) \text{ NC}^{-1}$$ exists in space. A cube of side $$2 \text{ m}$$ is placed in the space as per figure given below.

The electric flux through the cube is ______ $$\text{Nm}^2/\text{C}$$.