Electrostatics - JEE Advanced PYQ | Last 5 years | PYQ Khazana #jeeadvancedPYQ

Two beads, each with charge q and mass m, are on a horizontal, frictionless, non-conducting, circular hoop of radius R. One of the beads is glued to the hoop at some point, while the other one performs small oscillations' about its equilibrium position along the hoop. The square of
the angular frequency of the small oscillations is given by [ε0 is the permittivity of free space.]

A small electric dipole po, 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 o is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle 0 as shown in the figure. While
staying at a distance r, the dipo(e is free to rotate about its center.

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 1/4πEo = 9 x 109 , In 2 = 0.7. Ignore the area pierced by the wire.]

An electric dipole is formed by two charges +q and -q located in xy-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 dipole is Vo. The charges +q and -q are then moved to the points (-1,2) mm and
(1,-2) mm, respectively. What is the value of electric potential at P due to the new dipole?

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 the center O of the hexagon and is bisected
by the side.

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

A disk of radius R with uniform positive charge density o is placed on the xy plane with its center at
the origin. The Coulomb potential along the z-axis is A particle of positive charge q is placed initially at rest at a point on the z axis with z = zo and Zo 0. In addition to the Coulomb force, the particle experiences a vertical force. Which of the following statement(s) is(are) correct?

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 a. The spheres are now immersed in a dielectric liquid of density 800 kg m-3
and dielectric constant 21. If the angle between the strings remains the same after the immersion,
then

A uniform electric field, E =- 400v39 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 2v10 x 106 ms-1. This
particle is aimed to hit a target T, which is 5 m away from its entry point into the field as shown
schematically in the figure. Take 4 = 10 Ckg-1. Then

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JEE Advanced PYQ
Electrostatics

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