Two charges each equal to $\eta q({\eta ^{ – 1}} < \sqrt 3 )$ are placed at the corners of an equilateral triangle of side $a$. The electric field at the third corner is ${E_3}$ where $({E_0} = q/4\pi {\varepsilon _0}{a^2})$

A charged particle of mass $0.003\, gm$ is held stationary in space by placing it in a downward direction of electric field of $6 \times {10^4}\,N/C$. Then the magnitude of the charge is

A charged spherical drop of mercury is in equilibrium in a plane horizontal air capacitor and the intensity of the electric field is $6 × 10^4 $  $Vm^{-1}$. The charge on the drop is $8 × 10^{-18}$ $C$. The radius of the drop is $\left[ {{\rho _{air}} = 1.29\,kg/{m^3};{\rho _{Hg}} = 13.6 \times {{10}^3}kg/{m^3}} \right]$

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

The electric field in a region is radially outward and at a point is given by $E=250 \,r V / m$ (where $r$ is the distance of the point from origin). Calculate the charge contained in a sphere of radius $20 \,cm$ centred at the origin ……… $C$