$A$ charge $Q$ is uniformly distributed over the volume of an insulating sphere of radius $R$. $A$ thin metal shell of radius $b$ $(b > R)$ with a charge $-Q$ is placed around the sphere. The space between the sphere and the shell is filled with air. Which of the following graphs correctly represents the electric field $E$ as a function of distance $r$ from the center?

Two equal negative charges $-q$ each are fixed at the points $(0, a)$ and $(0, -a)$ on the $Y$-axis. $A$ positive charge $Q$ is released from rest at the point $(2a, 0)$ on the $X$-axis. The charge $Q$ will :-

$A$ solid sphere of radius $R$ carries a charge $(Q+q)$ distributed uniformly over its volume. $A$ very small point-like piece of it of mass $m$ gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge $q$. If it acquires a speed $v$ when it has fallen through a vertical height $y$ (see figure),then: (assume the remaining portion to be spherical).

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

$A$ negative point charge is placed at point $A$ as shown in the figure. The charge is:

In a regular polygon of $n$ sides,each corner is at a distance $r$ from the centre. Identical charges are placed at $(n - 1)$ corners. At the centre,the intensity is $E$ and the potential is $V$. The ratio $V/E$ has magnitude.