$A$ charge $Q$ is uniformly distributed over the surface of a thin spherical shell of radius $R$. Which of the following graphs most closely represents the electric field $E(r)$ produced by the shell in the range $0 \leq r < \infty$,where $r$ is the distance from the center of the shell?

Four charges $+Q, -Q, +Q, -Q$ are placed at the corners of a square taken in order. At the centre of the square:

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:

An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in the figure. If it is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the outer surface carries a uniform charge density $+\sigma$, if the inner surface of the shell is earthed, then identify the correct statement(s).

Two charged identical metal spheres $A$ and $B$ repel each other with a force of $3 \times 10^{-5} \,N$. Another identical uncharged sphere $C$ is touched with sphere $A$ and then it is placed mid-way between $A$ and $B$. Then, the magnitude of net force on $C$ is

$A$ particle of mass $m$ and charge $q$ is kept at the top of a fixed frictionless sphere. $A$ uniform horizontal electric field $E$ is switched on. The particle loses contact with the sphere when the line joining the center of the sphere and the particle makes an angle $45^{\circ}$ with the vertical. The ratio $\frac{qE}{mg}$ is: