A finite ladder is constructed by connecting several sections of $2\,\mu F$ , $4\,\mu F$ capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance $C$. What value should be chosen for $C$ such that the equivalent capacitance of the ladder between the points $A$ and $B$ becomes independent of the number of sections in between.......$\mu F$

A point charge $+Q$ is positioned at the centren of the base of a square pyramid as shown. The flux through one of the four identical upper faces of the pyramid 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?

Two equal $-ve$ charges $-q$ 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 will

Consider the situation shown. The switch $S$ is opened for a long time and then closed. The charge flown through the battery when $S$ is closed

In the given figure, three capacitors $C_1, C_2$ and $C_3$ are joined to a battery, with symbols having their usual meanings, the correct conditions will be