$A$ particle of mass $m$ and charge $q$ is thrown in a region where uniform gravitational field and electric field are present. The path of the particle:

Two identical non-conducting thin hemispherical shells,each of radius $R$,are brought into contact to form a complete sphere. If a total charge $Q$ is uniformly distributed on them,what is the minimum force $F$ required to hold them together?

$A$ Van de Graaff generator produces:

Two point positive charges are placed at a distance $d$ apart. $A$ third positive charge is placed at a distance $x$ on the perpendicular bisector. For what value of $x$ is the force on the third charge maximum?

One moving electron when comes closer to another stationary electron,then its kinetic energy and potential energy respectively . . . . . . and . . . . . . .

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.