In a regular polygon of $10$ sides,each corner is at a distance $R$ from the centre. Identical charges $q$ are placed at $9$ corners. At the centre,the magnitude of the electric field is $E$ and the potential is $V$. The ratio $\frac{V}{E}$ is

$A$ uniformly charged thin spherical shell of radius $R$ carries a uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $F$ (see figure). $F$ is proportional to

This question contains Statement-$1$ and Statement-$2$. Of the four choices given after the statements,choose the one that best describes the two statements.
Statement-$1$ : For a charged particle moving from point $P$ to point $Q$,the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q$.
Statement-$2$ : The net work done by a conservative force on an object moving along a closed loop is zero.

Two equal negative charges 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

Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatic forces are acting, which of the following statements is true?

An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in the figure. It is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the outer surface carries a uniform charge density $+\sigma$. If a point charge $q_A$ is placed at the center and another point charge $q_B$ is placed at a distance $c (> b)$ from the center of the shell,then choose the correct statement.