$A$ long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $-\sigma$ in the lower half. The electric field lines around the cylinder will look like the figure given in:

Three identical charges are placed at the three corners of an equilateral triangle as shown in the figure. Which of the following statements is true for the electric field $E$ and electric potential $V$ at the center $O$?

Let $E_1(r)$,$E_2(r)$,and $E_3(r)$ be the respective electric fields at a distance $r$ from a point charge $Q$,an infinitely long wire with constant linear charge density $\lambda$,and an infinite plane with uniform surface charge density $\sigma$. If $E_1(r_0) = E_2(r_0) = E_3(r_0)$ at a given distance $r_0$,then:

$A$ point charge $q$ moves from point $P$ to $S$ along the path $PQRS$ in a uniform electric field $E$ directed parallel to the positive $X$-axis. The coordinates of points $P, Q, R,$ and $S$ are $(a, b, 0), (2a, 0, 0), (a, -b, 0),$ and $(0, 0, 0)$ respectively. Calculate the work done by the electric field in this process.

Two identical positive charges are fixed on the $y$-axis, at equal distances from the origin $O$. $A$ particle with a negative charge starts on the $x$-axis at a large distance from $O$, moves along the $+x$-axis, passes through $O$, and moves far away from $O$. Its acceleration $a$ is taken as positive in the positive $x$-direction. The particle's acceleration $a$ is plotted against its $x$-coordinate. Which of the following best represents the plot?

For two electrons separated by a distance of $10 \, cm$,let $F_g$ and $F_e$ represent the gravitational force and electrostatic force between them,respectively. The ratio $F_g / F_e$ is of the order of: