Two equal point charges exert a force $F$ on each other when they are placed distance $d$ apart in air. When they are placed distance $D$ apart in a medium of dielectric constant $K$, they exert the same force. The distance $D$ is equal to

Three identical charges,each $2 \mu C$,lie at the vertices of a right-angled triangle as shown in the figure. Forces on the charge at $B$ due to the charges at $A$ and $C$ respectively are $F_1$ and $F_2$. The angle between their resultant force and $F_2$ is

Three charged particles of each mass $0.1 \,g$ and charge $q$ are suspended from a common rigid point by insulated massless threads of each $1 \,m$ long. If the three particles are in equilibrium and are located at the corners of an equilateral triangle of side $3 \,cm$, the charge $q$ on each particle is . . . . . . $nC$. (The angle made by the line joining the centroid of the triangle and the point of suspension with the vertical is very small). (Acceleration due to gravity $= 10 \,ms^{-2}$ and $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \,Nm^2 C^{-2}$)

What is the force between two small charged spheres having charges of $2 \times 10^{-7} C$ and $3 \times 10^{-7} C$ placed $30 cm$ apart in air?

Two charged spheres are suspended by strings of equal length. The strings make an angle of $30^{\circ}$ with each other. When suspended in a liquid of density $0.8 \ g/cm^3$,the angle remains the same. The dielectric constant of the liquid is ........ (The density of the material of the sphere is $1.6 \ g/cm^3$.)

Three point charges $+q$,$+2q$,and $+4q$ are placed along a straight line such that the charge $+2q$ is equidistant from the other two charges. The ratio of the net electrostatic force on charges $+q$ and $+4q$ is