A square plate of side $'a'$ is placed in $xy$ plane having centre at origin if charge density of square plate is $\sigma = xy$ then. Total charge on the plate will be.

Four metallic plates, each with a surface area of one side $A$, are placed at a distance $d$ from each other. The plates are connected as shown in the figure. The capacitance of  the system between $a$ and $b$ is

In the figure shown, the potential difference between points $A$ and $B$ is......$V$

A particle of charge $Q$ and mass $m$ travels through a potential difference $V$ from rest. The final momentum of the particle is

A charged particle with charge $q$ and mass $m$ starts with an initial kinetic energy $K$ at the centre of a uniformly charged spherical region of total charge $Q$ and radius $R$. Charges $q$ and $Q$ have opposite signs. The spherically charged region is not free to move and kinetic energy $K$ is just sufficient for the charge particle to reach boundary of the spherical charge. How much time does it take the particle to reach the boundary of the region?

Five balls marked a to $e$ are suspended using separate threads. Pairs $(b, c)$ and $(d, e)$ show electrostatic repulsion while pairs $(a, b),(c, e)$ and $(a, e)$ show electrostatic attraction. The ball marked a must be