Two point charges $+8q$ and $-2q$ are located at $x = 0$ and $x = L$ respectively. The location of a point on the $x-$ axis at which net electric field due to these two point charges is zero, is

Two identical point charges are placed at a separation of $ l.$ $P$ is a point on the line joining the charges, at a distance $x$ from any one charge. The field at $P$ is $E$. $E$ is plotted against $x$ for values of $x$ from close to zero to slightly less than $l$. Which of the following best represents the resulting curve?

Three plates of common surface area $A$ are connected as shown. The effective capacitance will be

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

The work done in placing a charge of $8 \times 10^{-18}$ coulomb on a condenser of capacity $100\, micro-farad$ is

Two identical balls having like charges and placed at a certain distance apart repel each other with a certain force. They are brought in contact and then moved apart to a distance equal to half their initial separation. The force of repulsion between them increases $4.5$ times in comparison with the initial value. The ratio of the initial charges of the balls is