A charged cork of mass $m$ suspended by a light string is placed in uniform electric filed of strength $E= $$(\hat i + \hat j)$ $\times$ $10^5$ $NC^{-1}$ as shown in the fig. If in equilibrium position tension in the string is $\frac{{2mg}}{{(1 + \sqrt 3 )}}$ then angle $‘\alpha ’ $ with the vertical is

Two point charges $( + Q)$ and $( - 2Q)$ are fixed on the $X-$axis at positions $a$ and $2a$ from origin respectively. At what positions on the axis, the resultant electric field is zero

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 point charges $Q$ and $-3Q$ are placed at some distance apart. If the electric field at the location of $Q$ is $E$ then at the locality of $ - 3Q$, it is

In the given figure distance of the point from $A$ where the electric field is zero is......$cm$

A wire of length $L\, (=20\, cm)$, is bent into a semicircular arc. If the two equal halves of the arc were each to be uniformly charged with charges $ \pm Q\,,\,\left[ {\left| Q \right| = {{10}^3}{\varepsilon _0}} \right]$ Coulomb where $\varepsilon _0$ is the permittivity (in $SI\, units$) of free space] the net electric field at the centre $O$ of the semicircular arc would be