Two electric charges $+2 \mu C$ and $-4 \mu C$ are separated by a distance $3 \ m$ in air. At a point $P$ located on the line joining the two charges and in between them, the electric potential is zero. Then the electric field at point $P$ (in $NC^{-1}$) is (in $,000$)

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

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 small spheres carry charges $Q_1$ and $Q_2$ $(Q_1 >> Q_2)$. The force between them is $F_1$. The spheres are brought into contact and then placed at the same distance. The new force between them is $F_2$. Then $F_1/F_2$ will be:

An uncharged metal sphere is placed between two charged parallel plates. Which of the following diagrams correctly represents the pattern of the electric field lines?

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 slowly moved inside the cavity of the shell,then choose the correct statement$(s)$.