Two identical charged spheres are suspended by string of equal lengths. The string make an angle of $37^{\circ}$ with each other. When suspended in a liquid of density $0.7 \mathrm{~g} / \mathrm{cm}^3$, the angle remains same. If density of material of the sphere is $1.4 \mathrm{~g} / \mathrm{cm}^3$, the dielectric constant of the liquid is_____$\left(\tan 37^{\circ}=\frac{3}{4}\right)$.

Three capacitors $A,B$ and $C$ are connected with battery $emf\, \varepsilon $. All capacitors are identical initially. If dielectric slab is inserted between plates of capacitor $A$ slowy with help of external force then 

Write the relation between $\vec P$ and $\vec E$ for a linear isotropic dielectric.

A parallel plate capacitor has a dielectric slab of dielectric constant $K$ between its plates that covers $1 / 3$ of the area of its plates, as shown in the figure. The total capacitance of the capacitor is $C$ while that of the portion with dielectric in between is $C _1$. When the capacitor is charged, the plate area covered by the dielectric gets charge $Q_1$ and the rest of the area gets charge $Q_2$. Choose the correct option/options, igonoring edge effects.

$(A)$ $\frac{E_1}{E_2}=1$ $(B)$ $\frac{E_1}{E_2}=\frac{1}{K}$ $(C)$ $\frac{Q_1}{Q_2}=\frac{3}{K}$ $(D)$ $\frac{ C }{ C _1}=\frac{2+ K }{ K }$

The expression for the capacity of the capacitor formed by compound dielectric placed between the plates of a parallel plate capacitor as shown in figure, will be (area of plate $ = A$)

The area of each plate of a parallel plate capacitor is $100\,c{m^2}$and the distance between the plates is $1\,mm$. It is filled with mica of dielectric $6$. The radius of the equivalent capacity of the sphere will be.......$m$