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 the net electric field due to these two point charges is zero is

A network of four capacitors of capacity equal to $C_1 = C, C_2 = 2C, C_3 = 3C$ and $C_4=4C$ are conducted to a battery as shown in the figure. The ratio of the charges on $C_2$ and $C_4$ is

Electric potential at an equatorial point of a small dipole with dipole moment $P$  ( $r$ , distance from the dipole) is

Two equal point charges are fixed at $x = -a$ and $x = + \,a$ on the $x$-axis. Another  point charge $Q$ is placed at the origin. The change in the electrical potential energy of $Q$ ehen it is displaced by a small distance $x$ along the $x$ -axis is apporximately proportional to

Two identical parallel plate capacitor are placed in series and connected to a constant voltage source of $V_0\, volt$. If one of the capacitors is completely immersed in a liquid with dielectric constant $K$, the potential difference between the plates of the other capacitor will change to