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 $\gamma$. The system of charges and the planar film are in equilibrium,and $a = k \left[ \frac{q^2}{\gamma} \right]^{1/N}$,where $k$ is a constant. Then $N$ is:

The force between two conducting spheres of same radius having charges $+8 \mu C$ and $-4 \mu C$ separated by some distance in air is $F$. If the spheres are connected by a conducting wire and after some time the wire is removed,then the magnitude of the force between the two conducting spheres is

$A$ long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $-\sigma$ in the lower half. The electric field lines around the cylinder will look like the figure given in:

In the following four situations,charged particles are at an equal distance from the origin. Arrange them in order of the magnitude of the net electric field at the origin,starting from the greatest.

Two equal negative charges $-q$ are placed at points $(0, a)$ and $(0, -a)$ on the $Y$-axis. A positive charge $q$ is released from rest at point $(2a, 0)$. What will be the motion of this charge?

In $1959$,Lyttleton and Bondi suggested that the expansion of the Universe could be explained if matter carried a net charge. Suppose that the Universe is made up of hydrogen atoms with a number density $N$,which is maintained constant. Let the charge on the proton be: $e_p = -(1 + y)e$,where $e$ is the electronic charge.
$(a)$ Find the critical value of $y$ such that expansion may start.
$(b)$ Show that the velocity of expansion is proportional to the distance from the centre.