A parallel plate capacitor with air between the plates has a capacitance of  $9\ pF$ . The separation between its plates is $ 'd'$ .The space between the plates is now filled with two dielectrics. One of the dielectric has dielectric constant $K_1 = 6$ and thickness $\frac {d}{3}$ while the other one has dielectric constant $K_2 = 12$ and thickness $\frac {2d}{3}$ . Capacitance of the capacitor is now ......... $pF$

A parallel plate capacitor of area $A$, plate separation $d$ and capacitance $C$ is filled with three different dielectric materials having dielectric constant $K_1,K_2$ and $K_3$ as shown. If a single dielectric material is to be used to have the same capacitance $C$ in this capacitor, then its dielectric constant $K$ is given by: ($A =$ Area of plates)

A charge $q$ is placed at the centre of cubical box of side a with top open. The flux of the electricn field through one of the surface of the cubical box is

If the electric flux entering and leaving an enclosed surface respectively is ${\phi _1}$ and  ${\phi _2}$ the electric charge inside the surface will be 

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

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