How much work is done in moving a charge $+q$ once around a circle of radius $r$ in the presence of a central charge $+Q$?

Four charges $2C, -3C, -4C$ and $5C$ respectively are placed at the corners of a square of side length $L$. Which of the following statements is true for the point of intersection of the diagonals?

$A$ charged cork of mass $m$ suspended by a light string is placed in a uniform electric field of strength $E = (\hat{i} + \hat{j}) \times 10^5 \ NC^{-1}$ as shown in the figure. If in the equilibrium position,the tension in the string is $\frac{2mg}{(1 + \sqrt{3})}$,then the angle $\alpha$ with the vertical is:

Six charges,three positive and three negative of equal magnitude,are to be placed at the vertices of a regular hexagon such that the electric field at $O$ is double the electric field when only one positive charge of the same magnitude is placed at $R$. Which of the following arrangements of charges is possible for $P, Q, R, S, T,$ and $U$ respectively?

The time period of a block of mass $m$ suspended from the upper plate of a parallel plate capacitor by a spring of stiffness $k$ is $T$ when the block is uncharged. If a charge $q$ is given to the block,what will be the new time period of oscillation?

Four equal positive charges are fixed at the vertices of a square of side $L$. The $Z$-axis is perpendicular to the plane of the square. The point $z = 0$ is the point where the diagonals of the square intersect. Find the plot of the electric field $E$ due to the four charges as one moves along the $Z$-axis.