Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $45^{\circ}$ with each other. When the system is immersed in a liquid of relative density 0.8 , the angle between the strings remains unchanged. If the density of the material of the sphere is $2.4 \mathrm{gcm}^{-3}$, what is the dielectric constant of the liquid?

Two conducting spherical shells $A$ and $B$ of radii 4 cm and 6 cm respectively are placed with their centres 17 cm apart in air. Initially, sphere A was given a -20 nC charge while sphere B was uncharged. The spheres are then connected by a long thin conducting wire and allowed to reach electrostatic equilibrium. Assuming no charge is lost to the surroundings, the final charge on sphere A and the ratio of magnitude of electric field intensity at the surface of sphere $B$ to that of sphere $A$ is given by;

A uniform electric field $E=3 \hat{i}+6 \hat{j}+\hat{k}$ passes through a closed cuboidal surface. One face of the cuboid has an area $4 m^2$ and an outward unit normal given by $\frac{2 \hat{i}+2 \hat{j}+3 \hat{k}}{\sqrt{17}}$. If the electric flux through the remaining 5 faces is zero, the charge enclosed by the cuboid is:

Point charge $\sqrt{2} C, \sqrt{2} C$, and $-2 C$ are placed at the three vertices of a right-angled triangle in air. [as shown in the figure below]

What is the electric field at a point $P$ on the hypotenuse that is equidistant from all three charges.

Given distances $X P=Y P=Z P=0.5 \mathrm{~m}$