  Previous Year Questions

## Electric Charges And Fields

- It's good to be already prepared. Go through the previous year questions
1
JEE Mains
Let a total charge be distributed in a sphere of radius , with the charge density given by , where is the distance from the centre. Two charges and , of each, are placed on diametrically opposite points, at equal distance, a form the centre. If and do not experience any force, then:
A
B
C
D

Two infinite planes each with uniform surface charge density are kept in such a way that the angle between them is . The electric field in the region shown between them is given by :

A
B
C
D
A particle of mass and charge is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed on the distance travelled by it is correctly given by (graphs are schematic and not drawn to scale)
A
B
C
D
In finding the electric field using Gauss law the formula is applicable. In the formula is permittivity of free space, is the area of Gaussian surface and is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation?
A
For any choice of Gaussian surface.
B
Only when the Gaussian surface is an equipotential surface and is constant on the surface.
C
Only when constant on the surface.
D
Only when the Gaussian surface is an equipotential surface.
Three charged particles and with charges and are present on the circumference of a circle of radius . The charged particles and centre of the circle formed an equilateral triangle as shown in figure. Electric field at along x-direction is:
A
B
C
D
An electric dipole of moment C.m is at the origin . The electric field due to this dipole at (note that is parallel to):
A
B
C
D
An electric field passes through the box shown in figure. The flux of the electric field through surfaces and are marked as and respectively. The difference between is (in
A body of mass and charge is connected to a spring of spring constant . It is oscillating along x-direction about its equilibrium position, taken to be at , with an amplitude . An electric field is applied along the x-direction. Which of the following statements is correct?
A
The total energy of the system is
B
The new equilibrium position is at a distance: from
C
The new equilibrium position is at a distance: from
D
The total energy of the system is
A charge is placed at a distance above the centre of the square surface of edge as shown in the figure.
The electric flux through the square surface is:
A
B
C
D
Four closed surface and corresponding charges distributions are shown below:
Let the respective electric fluxes through the surfaces be , , and . Then :
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B
C
D
2
Let E(r), E(r) and E(r) be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density , and an infinite plane with uniform surface charge density . If E at a given distance r, then :
A
B
C
D

A point charge is placed just outside an imaginary hemispherical surface of radius as shown in the figure. Which of the following statements is/are correct?
This question has multiple correct options
A
The electric flux passing through the curved surface of the hemisphere is
B
The component of the electric field normal to the flat surface is constant over the surface
C
Total flux through the curved and the flat surface is
D
The circumference of the flat surface is an equipotential
A particle of mass kg and charge C, is initially at rest. At time , the particle comes under the influence an electric field where and . Consider the effect of only the electrical force on the particle. Then the maximum speed, in , attained by the particle at subsequent times is __________.
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 relations between E and d. List - II describes different electric charge distributions, along with their locations. Match the functions in List - I with the related charge distributions in List - II

 List - I List - II (P) E is independent of d (1) A point charge Q at the origin (Q) (2) A small dipole with point charges Q at and - Q at (0, 0, -l). Take (R) (3) A infinite line charge coincident with the x-axis, with uniform linear charge density . (S) (4) Two infinite wires carrying uniform linear charge density parallel to the x-axis. The one along () has a charge density + and the one along has a charge density . Take (5) Infinite plane charge coincident with the xy-plane with uniform surface charge density.

A
B
C
D
A charged shell of radius R carries a total charge Q. Given as the flux of electric field through a closed cylindrical surface of height h, radius r and with its centre same as that of the shell. Here center of cylinder is a point on the axis of the cylinder which is equidistant from its top and bottom surfaces. Which of the following option(s) is are correct? is the permittivity of free space
This question has multiple correct options
A
If and then
B
If and then
C
If and then
D
If and then
A uniform electric field, 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 . 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 . Then
This question has multiple correct options
A
the particle will hit T if projected at an angle from the horizontal
B
the particle will hit T if projected either at an angle or from the horizontal
C
time taken by the particle to hit T could be us as well as
D
time taken by the particle to hit T is
A circular disc of radius R carries surface charge density where is a constant and 𝑟 is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is . Electric flux through another spherical surface of radius and concentric with the disc is . Then the ratio is________.
A cubical region of side a has its centre at the origin. It encloses three fixed point charges, -q
at (0, -a/4, 0), +3q at (0, 0, 0) and -q at (0, +a/4 ,0). Choose the correct option(s):
This question has multiple correct options
A
The net electric flux crossing the plane x = +a/2 is equal to the net electric flux crossing the plane x = -a/2
B
The net electric crossing the plane y = +a/2 is more than the net electric flux crossing the plane y = -a/2
C
The net electric flux crossing the entire region is
D
The net electric flux crossing the piane z = +a/ 2 is equal to the riet electric flux crossing the piane x = +a/2
An infinitely long solid cylinder of radius R has a uniform volume charge density . it has a spherical cavity of radius R/2 with its center on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point P, which is at a distance 2R from the axis of the cylinder, is given by the expression . The value of k is:
A
6
B
7
C
8
D
9
Two charges, each equal to , are kept at and on the -axis. A particle of mass and charge is placed at the origin. If charge is given a small displacement along the -axis, the net force acting on the particle is proportional to:

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D