Consider the points lying on a straight line joining two fixed opposite charges. Between the charges,there is:

$A$ charge $q$ is placed in the middle of a line joining two equal and like point charges $Q$. For what value of $q$ will the system be in equilibrium?

$A$ negatively charged plate has a surface charge density of $2 \times 10^{-6} \, C/m^2$. Find the minimum initial distance of an electron moving toward the plate such that it does not strike the plate,given that its initial kinetic energy is $200 \, eV$.

$A$ pendulum bob of mass $30.7 \times 10^{-6} \, kg$ and carrying a charge $2 \times 10^{-8} \, C$ is at rest in a horizontal uniform electric field of $20000 \, V/m$. The tension in the thread of the pendulum is $(g = 9.8 \, m/s^2)$.

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

When two spheres having $4 Q$ and $-2 Q$ charge are placed at a certain distance,the force acting between them is $F$. Now they are connected by a conducting wire and again separated from each other. Now they are kept at a distance half of the previous one. The force acting between them is . . . . . . .