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Electrostatics

65 questions · Physics · JEE Advanced

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JEE Advanced
Physics
Electrostatics

Electrostatics

65 questions · Physics · JEE Advanced

List-I shows four configurations, each consisting of a pair of ideal electric dipoles. Each dipole has a dipole moment of magnitude $p$ , oriented as marked by arrows in the figures. In all the configurations the dipoles are fixed such that… Includes table Includes diagram2025 · Shift 1 · Q46 · MCQ
Two co-axial conducting cylinders of same length $ℓ$ with radii $2 R$ and $2 R$ are kept, as shown in Fig. 1. The charge on the inner cylinder is $Q$ and the outer cylinder is grounded. The annular region between the cylinders is… Includes diagram2025 · Shift 2 · Q34 · MCQ
A positive point charge of $1 0^{- 8}$ C is kept at a distance of 20 cm from the center of a neutral conducting sphere of radius 10 cm. The sphere is then grounded and the charge on the sphere is measured. The grounding is then removed and…2025 · Shift 2 · Q37 · Multiple correct
Six infinitely large and thin non-conducting sheets are fixed in configurations I and II. As shown in the figure, the sheets carry uniform surface charge densities which are indicated in terms of $σ_{0}$ . The separation between any two… Includes diagram2025 · Shift 2 · Q39 · Multiple correct
Two beads, each with charge $q$ and mass $m$ , are on a horizontal, frictionless, non-conducting, circular hoop of radius $a$ . One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its…2024 · Shift 1 · Q37 · MCQ
A small electric dipole $p_{0}$ , having a moment of inertia $I$ about its center, is kept at a distance $r$ from the center of a spherical shell of radius $R$ . The surface charge density $σ$ is uniformly distributed on the… Includes diagram2024 · Shift 2 · Q39 · Multiple correct
A charge is kept at the central point $P$ of a cylindrical region. The two edges subtend a half-angle $θ$ at $P$ , as shown in the figure. When $θ = 3 0^{\circ}$ , then the electric flux through the curved surface of… Includes diagram2024 · Shift 2 · Q44 · Numerical
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 $10 nC$ , as shown in the figure. A $10 nC$ charge is distributed… Includes diagram2024 · Shift 2 · Q46 · Numerical
An electric dipole is formed by two charges $+ q$ and $- q$ located in $x y$ -plane at $(0, 2) mm$ and $(0, - 2) mm$ , respectively, as shown in the figure. The electric potential at point $P (100, 100) mm$ due to the… Includes diagram2023 · Shift 2 · Q35 · MCQ
Six charges are placed around a regular hexagon of side length $a$ as shown in the figure. Five of them have charge $q$ , and the remaining one has charge $x$ . The perpendicular from each charge to the nearest hexagon side passes through… Includes diagram2022 · Shift 1 · Q49 · Multiple correct
A charge $q$ is surrounded by a closed surface consisting of an inverted cone of height $h$ and base radius $R$ , and a hemisphere of radius $R$ as shown in the figure. The electric flux through the conical surface is $\frac{n q}{6 ϵ _{0}}$ … Includes diagram2022 · Shift 2 · Q42 · Numerical
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 $ρ_{A} = k r$ , where $k$ is positive. In the… Includes diagram2022 · Shift 2 · Q45 · Multiple correct
A disk of radius $R$ with uniform positive charge density $σ$ is placed on the $x y$ plane with its center at the origin. The Coulomb potential along the $z$ -axis is $V (z) = \frac{σ}{2 ϵ _{0}} (R^{2} + z^{2} - z) .$ …2022 · Shift 2 · Q48 · Multiple correct
Two point charges $-$ Q and +Q/ $3$ are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius R and potential V = 0 in the xy-plane with… Includes diagram2021 · Shift 1 · Q47 · Numerical
Two point charges $-$ Q and +Q/ $3$ are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius R and potential V = 0 in the xy-plane with… Includes diagram2021 · Shift 1 · Q48 · Numerical
A circular disc of radius R carries surface charge density $σ (r) = σ_{0} (1 - \frac{r}{R})$ , where $σ$ 0 is a constant and r is the distance from the center of the disc. Electric flux through a…2020 · Shift 1 · Q40 · Numerical
One end of a spring of negligible unstretched length and spring constant k is fixed at the origin (0, 0). A point particle of mass m carrying a positive charge q is attached at its other end. The entire system is kept on a smooth… Includes diagram2020 · Shift 1 · Q44 · Numerical
A uniform electric field, $E = - 4003 y$ NC−1 is applied in a region. A charged particle of mass m carrying positive charge q is projected in this region with an initial speed of 2 $10 \times$ 106… Includes diagram2020 · Shift 1 · Q54 · Multiple correct
Two large circular discs separated by a distance of 0.01 m are connected to a battery via a switch as shown in the figure. Charged oil drops of density 900 kg m−3 are released through a tiny hole at the center of the top disc. Once some… Includes diagram2020 · Shift 2 · Q38 · Numerical
A point charge q of mass m is suspended vertically by a string of length l. A point dipole of dipole moment $p$ is now brought towards q from infinity so that the charge moves away. The final equilibrium position of the… Includes diagram2020 · Shift 2 · Q39 · Numerical
Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is $α$ . The spheres are…2020 · Shift 2 · Q47 · Multiple correct
A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential at its surface is V0. A hole with a small area $α$ 4 $π$ R2( $α$ << 1) is made on the shell without affecting the…2019 · Shift 1 · Q39 · MCQ
A charged shell of radius R carries a total charge Q. Given $ϕ$ as the flux of electric field through a closed cylindrical surface of height h, radius r and with its center same as that of the shell. Here, center of the cylinder is a…2019 · Shift 1 · Q46 · Multiple correct
An electric dipole with dipole moment $\frac{p _{0}}{2} (i + j)$ is held fixed at the origin O in the presence of a uniform electric field of magnitude E0. If the potential is constant on a circle of radius R… Includes diagram2019 · Shift 2 · Q37 · Multiple correct
A particle, of mass $1 0^{- 3} k g$ and charge $1.0 C,$ is initially at rest. At time $t = 0,$ the particle comes under the influence of an electric field $E (t) = E_{0} sin$ $ω t i,$ where $E_{0} = 1.0 N C^{- 1}$ …2018 · Shift 2 · Q37 · Numerical
An infinitely long thin non-conducting wire is parallel to the $z$ -axis and carries a uniform line charge density $λ .$ It pierces a thin non-conducting spherical shell of radius $R$ in such a way that the arc $P Q$ subtends an angle $12 0^{\circ}$ … Includes diagram2018 · Shift 2 · Q39 · Multiple correct
The electric field $E$ is measured at a point $P (0, 0, d)$ generated due to various charge distributions and the dependence of $E$ on $d$ is found to be different for different charge distributions. List- $I$ contains different… Includes table2018 · Shift 2 · Q51 · MCQ
A point charge $+ Q$ is placed just outside an imaginary hemispherical surface of radius $R$ as shown in the figure. Which of the following statements is/are correct? Includes diagram2017 · Shift 2 · Q37 · Multiple correct
Consider an evacuated cylindrical chamber of height h having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with… Includes diagram2016 · Shift 2 · Q53 · MCQ
Consider an evacuated cylindrical chamber of height h having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with… Includes diagram2016 · Shift 2 · Q54 · MCQ
The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density $λ$ are kept parallel to each other. In their resulting electric field, point charges $q$ and $- q$ are… Includes diagram2015 · Shift 1 · Q41 · Multiple correct
An infinitely long uniform line charge distribution of charge per unit length $λ$ lies parallel to the y-axis in the y-z plane at $z = \frac{3}{2}$ a (see figure). If the magnitude of the flux of the electric field through… Includes diagram2015 · Shift 1 · Q49 · Numerical
Consider a uniform spherical charge distribution of radius $R_{1}$ centred at the origin $O .$ In this distribution, a spherical cavity of radius $R_{2},$ centred at $P$ with distance $O P = a = R_{1} - R_{2}$ (see figure) is made. If the… Includes diagram2015 · Shift 2 · Q41 · Multiple correct
Let $E_{1} (r), E_{2} (r)$ and $E_{3} (r)$ be the respective electric field at a distance $r$ from a point charge $Q,$ an infinitely long wire with constant linear charge density $λ,$ and an…2014 · Shift 1 · Q43 · Multiple correct
Charges $Q, 2 Q$ and $4 Q$ are uniformly distributed in three dielectric solid spheres $3$ and $3$ of radii $R /2, R$ and $2 R$ respectively, as shown in figure. If magnitude of the electric fields at point $P$ at a distance $R$ from the… Includes diagram2014 · Shift 2 · Q41 · MCQ
Four charges Q1, Q2, Q3 and Q4 of same magnitude are fixed along the x axis at x = $-$ 2a, $-$ a, +a and +2a, respectively. A positive charge q is placed on the positive y axis at a distance b > 0. Four options of the signs of these… Includes table Includes diagram2014 · Shift 2 · Q58 · MCQ
Two non-conducting solid spheres of radii $R$ and $2 R,$ having uniform volume charge densities $ρ_{1}$ and $ρ_{2}$ respectively, touch each other. The net electric field at a distance $2 R$ from the center of the smaller sphere,…2013 · Shift 1 · Q50 · MCQ
Two non-conducting spheres of radii $R_{1}$ and $R_{2}$ and carrying uniform volume charge densities $+ ρ$ and $- ρ,$ respectively, are placed such that they partially overlap, as shown in the figure. At all points in the… Includes diagram2013 · Shift 2 · Q41 · Multiple correct
A cubical region of side $a$ has its center at the origin. It encloses three fixed point charges, $- q$ at $(0, - a /4, 0), + 3 q$ at $(0, 0, 0)$ and $- q$ at $(0, + a /4, 0) .$ Choose the correct… Includes diagram2012 · Shift 1 · Q41 · Multiple correct
Consider a thin spherical shell of radius $R$ with center at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field $E (r)$ and the…2012 · Shift 1 · Q42 · MCQ
Two large vertical and parallel metal plates having a separation of $1 c m$ are connected to a $D C$ voltage source of potential difference $X$ . A proton is released at rest midway between the two plates. It is found to move at $4 5^{\circ}$ …2012 · Shift 1 · Q43 · MCQ
An infinitely long solid cylinder of radius R has a uniform volume charge density $ρ$ . It has a spherical cavity of radius R/2 with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at… Includes diagram2012 · Shift 1 · Q57 · Numerical
Six point charges are kept at the vertices of a regular hexagon of side $L$ and center $O,$ as shown in the figure. Given that $K = \frac{1}{4 π ε _{0}} \frac{q}{L ^{2}},$ which of the following statement(s) is (are) correct… Includes diagram2012 · Shift 2 · Q42 · Multiple correct
Consider an electric field $E = E_{0} x$ where $E_{0}$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is Includes diagram2011 · Shift 1 · Q55 · MCQ
A spherical metal shell A of radius $R_{A}$ and a solid metal sphere $B$ of radius $R_{B} (< R_{A})$ are kept far apart and each is given charge $^{'} + Q^{'} .$ Now they are connected by a thin metal wire. Then2011 · Shift 1 · Q57 · Multiple correct
Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side a. The surface tension of the soap film is $γ$ . The system of charges and planar film are in equilibrium, and $a = k [\frac{q ^{2}}{γ}]^{1/ N}$ …2011 · Shift 1 · Q67 · Numerical
Which of the following statement(s) is/are correct?2011 · Shift 2 · Q41 · Multiple correct
Which of the field patterns given below is valid for electric field as well as for magnetic field ?2011 · Shift 2 · Q43 · MCQ
A few electric field lines for a system of two charges $Q_{1}$ and $Q_{2}$ fixed at two different points on the $x$ -axis are shown in the figure. These lines suggest that Includes diagram2010 · Shift 1 · Q65 · Multiple correct
A tiny spherical oil drop carrying a net charge $q$ is balanced in still air with a vertical uniform electric field of strength $\frac{81 π}{7} \times 1 0^{5} V m^{- 1} .$ When the field is switched off, the drop is observed to fall…2010 · Shift 2 · Q45 · MCQ
A uniformly charged thin spherical shell of radius $R$ carries uniform surface charge density of $σ$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $F$ (see figure). $F$ is proportional… Includes diagram2010 · Shift 2 · Q46 · MCQ
A disk of radius $\frac{a}{4}$ having a uniformly distributed charge 6C is placed in the xy-plane with its centre at ( $-$ a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x = a/4 to x =… Includes diagram2009 · Shift 1 · Q45 · MCQ
Three concentric metallic spherical shells of radii $R, 2 R, 3 R$ are given charges $Q_{1}, Q_{2}, Q_{3}$ , respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given…2009 · Shift 1 · Q46 · MCQ
Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column II. In each case, a point M and a line PQ passing through M are shown. Let E be the electric field and V be the electric potential at M… Includes table Includes diagram2009 · Shift 1 · Q60 · MCQ
A solid sphere of radius R has a charge Q distributed in its volume with a charge density $ρ = K r^{a}$ , where K and a are constants and r is the distance from its centre. If the electric field at $r = R /2$ is 1/8 times than at $r = R$ ,…2009 · Shift 2 · Q55 · Numerical
Consider a system of three charges $\frac{q}{3}, \frac{q}{3}$ and $- \frac{2 q}{3}$ placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60 $^{\circ}$ Includes diagram2008 · Shift 2 · Q46 · MCQ
A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2. The level of liquid is $\frac{d}{3}$ initially. Suppose the liquid level decreases at a constant speed V, the time… Includes diagram2008 · Shift 2 · Q53 · MCQ
STATEMENT 1 : For practical purposes, the earth is used as a reference at zero potential in electrical circuits. and STATEMENT 2 : The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given…2008 · Shift 2 · Q56 · MCQ
The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $ρ (r)$ [charge per unit volume] is dependent only on the radical distance r from the centre of the nucleus as shown in figure. The… Includes diagram2008 · Shift 2 · Q58 · MCQ
The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $ρ (r)$ [charge per unit volume] is dependent only on the radical distance r from the centre of the nucleus as shown in figure. The… Includes diagram2008 · Shift 2 · Q59 · MCQ
The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $ρ (r)$ [charge per unit volume] is dependent only on the radical distance r from the centre of the nucleus as shown in figure. The… Includes diagram2008 · Shift 2 · Q60 · MCQ
A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinder are initially electrically neutral.2007 · Shift 1 · Q48 · MCQ
Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,2007 · Shift 1 · Q49 · MCQ
A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is Includes diagram2007 · Shift 2 · Q14 · MCQ
Positive and negative point charges of equal magnitude are kept at $(0, 0, \frac{a}{2})$ and $(0, 0, \frac{- a}{2})$ , respectively. The work done by the electric field when another positive point charge is moved from…2007 · Shift 2 · Q15 · MCQ