JEE Electric Charges & Fields PYQs with Solutions PDF

Two point dipoles of dipole moment $$\vec{p_1}$$ and $$\vec{p_2}$$ are at a distance x from each other and $$\vec{p_1} \| \vec{p_2}$$. The force between the dipoles is :

Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities $$+\sigma$$, $$-\sigma$$ and $$+\sigma$$ respectively. The potential of shell B is:

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 $$V(R(t))$$ of the distribution as a function of its instantaneous radius $$R(t)$$ is:

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

Two electric dipoles, A, B with respective dipole moments $$\vec{d_A} = -4qa\hat{i}$$ and $$\vec{d_B} = -2qa\hat{i}$$ are placed on the $$x$$-axis with a separation $$R$$, as shown in the figure.

The distance from A at which both of them produce the same potential is:

An infinite number of point charges, each carrying $$1 \mu C$$ charge, are placed along the y-axis at $$y = 1$$ m, 2 m, 4 m, 8 m .....
The total force on a 1 C point charge, placed at the origin, is $$x \times 10^3$$ N. The value of $$x$$, to the nearest integer, is ___.
[Take $$\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9$$ N m$$^2$$ C$$^{-2}$$]

An infinitely long thin wire, having a uniform charge density per unit length of 5 nC/m, is passing through a spherical shell of radius 1 m, as shown in the figure. A 10 nC charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points $$P$$ and $$R$$, in Volt, is ________.

[Given: In SI units $$\dfrac{1}{4\pi \varepsilon_0} = 9 \times 10^9$$, ln 2 = 0.7. Ignore the area pierced by the wire.]

A charge Q is placed at a distance $$\frac{a}{2}$$ above the centre of a square surface of edge a as shown in the figure. The electric flux through the square surface is:

A stream of positively charged particles having $$\frac{q}{m} = 2 \times 10^{11}$$ C kg$$^{-1}$$ and velocity $$\vec{v_0} = 3 \times 10^7 \hat{i}$$ m s$$^{-1}$$ is deflected by an electric field $$1.8\hat{j}$$ kV m$$^{-1}$$. The electric field exists in a region of 10 cm along $$x$$ direction. Due to the electric field, the deflection of the charge particles in the $$y$$ direction is _____ mm.

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 _____.

A uniform electric field of 10 N C$$^{-1}$$ is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle ($$\theta$$) of deviation of the path of electron as it comes out of the field is _____ (in degree).

A point charge $$2 \times 10^{-2}$$ C is moved from $$P$$ to $$S$$ in a uniform electric field of $$30$$ N C$$^{-1}$$ 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

Four point charges -q, +q, +q and -q are placed on y-axis at y = -2d, y = -d, and y = +2d, respectively. The magnitude of the electric field E at a point on the x-axis at x = D, with D >> d, will behave as:

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 $$E_0 = 4 \times 10^4 \text{ NC}^{-1} \text{ m}^{-1}$$. If $$a = 2$$ cm, the charge contained in the cubical volume is $$Q \times 10^{-14}$$ C. The value of $$Q$$ is ______.
(Take $$\epsilon_0 = 9 \times 10^{-12} \text{ C}^2 \text{ N}^{-1}\text{m}^{-2}$$)

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

A charged ball $$B$$ hangs from a silk thread $$S$$ which makes an angle $$\theta$$ with a large charged conducting sheet $$P$$, as show in the figure. The surface charge density $$\sigma$$ of the sheet is proportional to

An oil drop of the radius 2 mm with a density 3 g cm$$^{-3}$$ is held stationary under a constant electric field $$3.55 \times 10^5$$ V m$$^{-1}$$ in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? (consider $$g = 9.81$$ m s$$^{-2}$$).

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 V/m, then the value of $$Q$$ is _______ nC.
$$(\varepsilon_0 = 8.85 \times 10^{-12}$$ C$$^2$$/Nm$$^2$$ and $$\pi = 3.14)$$

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 $$\frac{a}{\sqrt{x}}$$. The value of $$x$$ is _____.

Four closed surfaces and corresponding charge distributions are shown below.

Let the respective electric fluxes through the surfaces be $$\phi_1$$, $$\phi_2$$, $$\phi_3$$ and $$\phi_4$$. Then:

A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength $$1 \times 10^5$$ N C$$^{-1}$$. If the charge on the particle is 40 $$\mu$$C and the initial velocity is 200 m s$$^{-1}$$, how much distance it will travel before coming to the rest momentarily

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: $$r > b$$)

An electron with kinetic energy $$K_1$$ enters between parallel plates of a capacitor at an angle $$\alpha$$ with the plates. It leaves the plates at angle $$\beta$$ with kinetic energy $$K_2$$. Then the ratio of kinetic energies $$K_1 : K_2$$ will be:

Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A): Non-polar materials do not have any permanent dipole moment.
Reason (R): When a non-polar material is placed in an electric field, the centre of the positive charge distribution of it's individual atom or molecule coincides with the centre of the negative charge distribution.
In the light of above statements, choose the most appropriate answer from the options given below.

Three charged particles A, 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 the figure. The electric field at the point O is

Consider a circular loop that is uniformly charged and has a radius $$a\sqrt{2}$$. 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 :

Find out the surface charge density at the intersection of point $$x = 3$$ m plane and $$x$$-axis, in the region of uniform line charge of 8 nC m$$^{-1}$$ lying along the $$z$$-axis in free space.

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 potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell.
Choose the correct answer :

In the figure, the inner (shaded) region A represents a sphere of radius $$r_A = 1$$, within which the electrostatic charge density varies with the radial distance $$r$$ from the center as $$\rho_A = kr$$, where $$k$$ is positive. In the spherical shell B of outer radius $$r_B$$, the electrostatic charge density varies as $$\rho_B = \dfrac{2k}{r}$$. Assume that dimensions are taken care of. All physical quantities are in their SI units.

Which of the following statement(s) is(are) correct?

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 sphere and $$Q$$ be the total charge on it. The electric field at any point on the spherical surface of radius $$r (< R)$$ is zero but the electric flux passing through this closed spherical surface of radius $$r$$ is not.
In the light of the above statements, choose the correct answer from the options given below:

A particle of charge $$q$$ and mass $$m$$ is subjected to an electric field $$E = E_0(1 - ax^2)$$ in the $$x$$-direction, where $$a$$ and $$E_0$$ are constants. Initially the particle was at rest at $$x = 0$$. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is: