In a regular polygon of $10$ sides,each corner is at a distance $R$ from the centre. Identical charges $q$ are placed at $9$ corners. At the centre,the magnitude of the electric field is $E$ and the potential is $V$. The ratio $\frac{V}{E}$ is

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^o$ with each other. When suspended in a liquid of density $1 \, g \, cm^{-3}$,the angle remains the same. If the density of the material of the sphere is $4/3 \, g \, cm^{-3}$,the dielectric constant of the liquid is:

Two particles each of mass $m$ and charge $q$ are separated by distance $r_1$ and the system is left free to move at $t = 0$. At time $t$,both the particles are found to be separated by distance $r_2$. The speed of each particle is

The diagram shows three infinitely long uniform line charges placed on the $X, Y$ and $Z$ axes with linear charge densities $2\lambda, 3\lambda$ and $\lambda$ respectively. The work done by an external agent in moving a unit positive charge from $(1, 1, 1)$ to $(0, 1, 1)$ is equal to:

Which of the following patterns of electric field lines is $NOT$ possible for an electrostatic field due to static charges?

Let $E_1(r)$,$E_2(r)$,and $E_3(r)$ be the respective electric fields at a distance $r$ from a point charge $Q$,an infinitely long wire with constant linear charge density $\lambda$,and an infinite plane with uniform surface charge density $\sigma$. If $E_1(r_0) = E_2(r_0) = E_3(r_0)$ at a given distance $r_0$,then: