In the given square $ABCD$,charges $q$,$2q$,$3q$,and $4q$ are placed at corners $A$,$B$,$C$,and $D$ respectively. What is the direction of the net electric field at the center $O$?

Answer carefully:
$(a)$ Two large conducting spheres carrying charges $Q_{1}$ and $Q_{2}$ are brought close to each other. Is the magnitude of electrostatic force between them exactly given by $Q_{1} Q_{2} / 4 \pi \varepsilon_{0} r^{2}$,where $r$ is the distance between their centres?
$(b)$ If Coulomb's law involved $1/r^{3}$ dependence (instead of $1/r^{2}$),would Gauss's law be still true?
$(c)$ $A$ small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point?
$(d)$ What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical?
$(e)$ We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there?
$(f)$ What meaning would you give to the capacitance of a single conductor?
$(g)$ Guess a possible reason why water has a much greater dielectric constant $(=80)$ than,say,mica $(=6)$?

$A$ 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 $200 \, eV$.

$A$ clock dial has point charges $-q, -2q, -3q, \ldots, -12q$ at the positions of the corresponding numbers on the dial respectively. The time at which the hour hand points in the direction of the net electric field at the centre of the dial is (Assume clock hands do not influence the net electric field). (in $:30$)

The charge per unit length of the four quadrants of the ring are $2\lambda$,$-2\lambda$,$\lambda$,and $-\lambda$ respectively. The electric field at the centre is

Two identical charged spheres suspended from a common point by two massless strings of lengths $l$ are initially at a distance $d$ $(d << l)$ apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result,the spheres approach each other with a velocity $v$. Then $v$ varies as a function of the distance $x$ between the spheres,as: