Three parallel metal plates,each of area $A$,are placed as shown in the figure. Charges $Q_1$,$Q_2$,and $Q_3$ are given to them. Edge effects are negligible. Calculate the charge on the two outermost surfaces '$a$' and '$f$'.

Electric charges $Q$ are placed on the $x$-axis at $x = 1, 2, 4, 8, \dots \text{meters}$ respectively. What are the electric field and electric potential at $x = 0$?

$A$ metallic shell has a point charge '$q$' kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of force?

Four charges are arranged at the corners of a square $ABCD$,as shown. The force on a $+ve$ charge kept at the centre of the square is

Two identical charged spheres suspended from a common point by two massless strings of length $l$ are initially a distance $d$ $(d \ll l)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result,the spheres approach each other with a velocity $v$. Then,as a function of distance $x$ between them,

Two charges,each equal to $q$,are kept at $x = -a$ and $x = a$ on the $x$-axis. $A$ particle of mass $m$ and charge $q_0 = \frac{q}{2}$ is placed at the origin. If charge $q_0$ is given a small displacement $(y << a)$ along the $y$-axis,the net force acting on the particle is proportional to