What is the magnitude of a point charge which produces an electric field of $2\, N/coulomb$ at a distance of $60\, cm$ $(1/4\pi {\varepsilon _0} = 9 \times {10^9}\,N - {m^2}/{C^2})$

Two point charges $Q_1, Q_2$ are fixed at $x = 0$ and $x = a$. Assuming that field strength is positive in the direction coinciding with the positive direction of $x$, then, which following option will be correct ?

Two point charge $-q$ and $+q/2$ are situated at the origin and at the point $(a, 0, 0)$ respectively. The point along the $X$ - axis where the electric field vanishes is

The distance between a proton and electron both having a charge $1.6 \times {10^{ - 19}}\,coulomb$, of a hydrogen atom is ${10^{ - 10}}\,metre$. The value of intensity of electric field produced on electron due to proton will be

Infinite charges of magnitude $q$ each are lying at $x =1,\, 2,\, 4,\, 8...$ meter on $X$-axis. The value of intensity of electric field at point $x = 0$ due to these charges will be

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