$A$ charge $Q$ is placed at each of the opposite corners of a square. $A$ charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero,then $\frac{Q}{q} = $ . . . . . .

The electric field due to a uniformly charged sphere of radius $R$ as a function of the distance from its center is represented by which of the following graphs?

Let $E_1(r)$,$E_2(r)$,and $E_3(r)$ be the respective electric fields at a distance $r$ from a point charge $Q$,an infinitely long wire with constant linear charge density $\lambda$,and an infinite plane with uniform surface charge density $\sigma$. If $E_1(r_0) = E_2(r_0) = E_3(r_0)$ at a given distance $r_0$,then:

Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(d, 0)$ respectively of a $(X, Y)$ coordinate system. Then:

$A$ 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 particles of mass $m$ carry a charge $Q$ each. Initially, one is at rest on a smooth horizontal plane and the other is projected along the plane directly towards the first particle from a large distance with speed $v$. The closest distance of approach is: