$15$ charges,each of value $q$,are placed on the $X$-axis at an equal distance of $0.5R$. The electric flux associated with a spherical closed surface of radius $1.5R$,which has one of the charges at its center,is:

In a cuboid of dimension $2 L \times 2 L \times L$,a charge $q$ is placed at the centre of the surface ' $S$ ' having an area of $4 L^2$. The flux through the opposite surface to ' $S$ ' is given by

At a distance $l$ from a uniformly charged long wire, a charged particle is thrown radially outward with a velocity $u$ in the direction perpendicular to the wire. When the particle reaches a distance $2l$ from the wire, its speed is found to be $\sqrt{2}u$. The magnitude of the velocity, when it is a distance $4l$ away from the wire is (ignore gravity)

Obtain the expression for the electric field due to:
$(i)$ An infinite plane sheet with uniform charge distribution.
$(ii)$ $A$ thin spherical shell with uniform charge distribution at a point outside it.
$(iii)$ $A$ thin spherical shell with uniform charge distribution at a point inside it.

Three infinitely long charged non-conducting sheets are placed as shown in the figure. The electric field at point $P$ is ($\sigma$ - charge density,$\epsilon_0$ - permittivity of free space).

Which of the following graphs shows the variation of electric field $E$ due to a hollow spherical conductor of radius $R$ as a function of distance $r$ from the centre of the sphere?