A tiny $0.50\, gm$ ball carries a charge of magnitude $10\, \mu C$. It is suspended by a thread in a downward electric field of intensity $300\, N/C$. If the charge on the ball is positive, then the tension in the string is

Two point charges of $20\,\mu \,C$ and $80\,\mu \,C$ are $10\,cm$ apart. Where will the electric field strength be zero on the line joining the charges from $20\,\mu \,C$ charge......$m$

Figure shows a rod ${AB}$, which is bent in a $120^{\circ}$ circular arc of radius $R$. A charge $(-Q)$ is uniformly distributed over rod ${AB}$. What is the electric field $\overrightarrow{{E}}$ at the centre of curvature ${O}$ ?

In the following four situations charged particles are at equal distance from the origin. Arrange them the magnitude of the net electric field at origin greatest first

Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is $\alpha$. The spheres are now immersed in a dielectric liquid of density $800 kg m ^{-3}$ and dielectric constant $21$ . If the angle between the strings remains the same after the immersion, then

$(A)$ electric force between the spheres remains unchanged

$(B)$ electric force between the spheres reduces

$(C)$ mass density of the spheres is $840 kg m ^{-3}$

$(D)$ the tension in the strings holding the spheres remains unchanged

A charged ball $B$ hangs from a silk thread $S$, which makes an angle $\theta $ with a large charged conducting sheet $P$, as shown in the figure. The surface charge density $\sigma $ of the sheet is proportional to