Point charge $q$ moves from point $P$ to point $S$ along the path $PQRS$ (figure shown) in a uniform electric field $E$ pointing coparallel to the positive direction of the $X – $axis. The coordinates of the points $P,\,Q,\,R$ and $S$ are $(a,\,b,\,0),\;(2a,\,0,\,0),\;(a,\, – b,\,0)$ and $(0,\,0,\,0)$ respectively. The work done by the field in the above process is given by the expression

The ratio of electrostatic and gravitational forces acting between electron and proton separated by a distance $5 \times {10^{ – 11}}\,m,$ will be (Charge on electron $=$ $1.6 \times 10^{-19}$ $C$, mass of electron = $ 9.1 \times 10^{-31}$ $kg$, mass of proton = $1.6 \times {10^{ – 27}}\,kg,$ $\,G = 6.7 \times {10^{ – 11}}\,N{m^2}/k{g^2})$

Two spherical, nonconducting, and very thin shells of uniformly distributed positive charge $Q$ and radius d are located a distance $10d$ from each other. A positive point charge $q$ is placed inside one of the shells at a distance $d/2$ from the center, on the line connecting the centers of the two shells, as shown in the figure. What is the net force on the charge $q $ ?

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 magnitude of electric force on $2\, \mu \,C$ charge placed at the centre $O$ of two  equilateral triangles each of side $10 \,cm$, as shown in figure is $P$. If charge $A, B, C, D, E$ and $F$ are $2\, \mu \,C, 2\, \mu \,C, 2\, \mu \,C,-2\, \mu \,C, -2\, \mu \,C, -2\, \mu \,C$   respectively, then $P$ is :…..$N$