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)
$\frac{1}{K} = \frac{1}{{{K_1}}} + \frac{1}{{{K_2}}} + \frac{1}{{2{K_3}}}$
$\frac{1}{K} = \frac{1}{{{K_1} + {K_2}}} + \frac{1}{{2{K_3}}}$
$K = \frac{{{K_1}{K_2}}}{{{K_1} + {K_2}}} + 2{K_3}$
$K = K_1 + K_2 + 2K_3$
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 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
The work done required to put the four charges together at the corners of a square of side $a$ , as shown in the figure is
An electric dipole is placed along the $x$ -axis at the origin $O.$ A point $P$ is at a distance of $20\, cm$ from this origin such that $OP$ makes an angle $\frac{\pi}{3}$ with the $x$ -axis. If the electric field at $P$ makes an angle $\theta$ with the $x$ -axis, the value of $\theta$ would 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
Two equal charges are separated by a distance $d$. A third charge placed on a perpendicular bisector at $x$ distance will experience maximum coulomb force when