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**JEE Mains**

Let a total charge $2Q$ be distributed in a sphere of radius $R$, with the charge density given by $ρ(r)=kr$, where $r$ is the distance from the centre. Two charges $A$ and $B$, of $−Q$ each, are placed on diametrically opposite points, at equal distance, a form the centre. If $A$ and $B$ do not experience any force, then:

Two infinite planes each with uniform surface charge density $+σ$ are kept in such a way that the angle between them is $30_{0}$. The electric field in the region shown between them is given by :

A particle of mass $m$ and charge $q$ is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed $v$ on the distance $x$ travelled by it is correctly given by (graphs are schematic and not drawn to scale)

In finding the electric field using Gauss law the formula $∣E∣=∈_{0}∣A∣q_{enc} $ is applicable. In the formula $∈_{0}$ is permittivity of free space, $A$ is the area of Gaussian surface and $q_{enc}$ is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation?

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 figure. Electric field at $O$ along x-direction is:

An electric dipole of moment $p =(−i^−3j^ +2k^)×10_{−29}$ C.m is at the origin $(0,0,0)$. The electric field due to this dipole at $r=+i^+3j^ +5k$ (note that $r⋅p =0$ is parallel to):

An electric field $E=4xi^−(y_{2}+1)j^ N/C$ passes through the box shown in figure. The flux of the electric field through surfaces $ABCD$ and $BCGF$ are marked as $ϕ_{I}$ and $ϕ_{II}$ respectively. The difference between $(ϕ_{I}−ϕ_{II})$ is (in $Nm_{2}/C)$

A body of mass $M$ and charge $q$ is connected to a spring of spring constant $k$. It is oscillating along x-direction about its equilibrium position, taken to be at $x=0$, with an amplitude $A$. An electric field $E$ is applied along the x-direction. Which of the following statements is correct?

A charge $Q$ is placed at a distance $a/2$ above the centre of the square surface of edge $a$ as shown in the figure.

The electric flux through the square surface is:

The electric flux through the square surface is:

Four closed surface and corresponding charges distributions are shown below:

Let the respective electric fluxes through the surfaces be $Φ_{1}$, $Φ_{2}$, $Φ_{3}$ and $Φ_{4}$. Then :

Let the respective electric fluxes through the surfaces be $Φ_{1}$, $Φ_{2}$, $Φ_{3}$ and $Φ_{4}$. Then :