Three charged particle $A, B$ and $C$ with charges $-4 q, 2 q$ and $-2 q$ are present on the circumference of a circle of radius $d$. the charged particles $A, C$ and centre $O$ of the circle formed an equilateral triangle as shown in figure. Electric field at $O$ along $x-$direction is
$\frac{2 \sqrt{3} q}{\pi \varepsilon_{0} d^{2}}$
$\frac{\sqrt{3} \mathrm{q}}{4 \pi \varepsilon_{0} \mathrm{d}^{2}}$
$\frac{3 \sqrt{3} \mathrm{q}}{4 \pi \varepsilon_{0} \mathrm{d}^{2}}$
$\frac{\sqrt{3} q}{\pi \varepsilon_{0} d^{2}}$
A pendulum bob of mass $30.7 \times {10^{ - 6}}\,kg$ and carrying a charge $2 \times {10^{ - 8}}\,C$ is at rest in a horizontal uniform electric field of $20000\, V/m$. The tension in the thread of the pendulum is $(g = 9.8\,m/{s^2})$
Two uniform spherical charge regions $S_1$ and $S_2$ having positive and negative charges overlap each other as shown in the figure. Point $O_1$ and $O_2$ are their centres and points $A, B, C$ and $D$ are on the line joining centres $O_1$ and $O_2$. Electric field from $C$ to $D$
Deutron and $\alpha - $ particle are put $1\,\mathop A\limits^o $ apart in air. Magnitude of intensity of electric field due to deutron at $\alpha - $ particle is
Obtain the equation of electric field at a point by system of $\mathrm{'n'}$ point charges.
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