The diagrams below show regions of equipotentials:

       (a)                   (b)                       (c)                  (d)

A positive charge is moved from A to B in each diagram.

Suppose the charge of a proton and an electron differ slightly. One of them is $-e,$ the other is $(e+\mathrm{\Delta }e).$ If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance $d$ (much greater than atomic size) apart is zero, then $\mathrm{\Delta }e$ is of the order of (Given mass of hydrogen, $m_h=1.67\times {10}^{-27} \mathrm{kg})$

Two infinitely long uniformly charged non conducting sheets of charge density $\sigma =\sqrt{2}{\epsilon }_0\times {10}^{-3}$  each are placed perpendicular to each other as shown in figure. What is the resultant electric field intensity at point

A uniformly charged rod of length $4\mathrm{cm}$ and linear charge density $\lambda =30\mu C/m$ is placed as shown in figure. Calculate the $x$-component of electric field at point $P$.

An electron falls from rest through a vertical distance $h$ in a uniform and vertically upward directed electric field $E$. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance $h$. The time of fall of the electron, in comparison to the time of fall of the proton is