A charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium, if $q$ is equal to
$ - \frac{Q}{2}$
$ - \frac{Q}{4}$
$ + \frac{Q}{4}$
$ + \frac{Q}{2}$
Electric flux through surface $s_1$ :-
The electric potential $V$ at any point $(x, y, z)$ (all in $metres$ ) in space is given by $V = 4x^2\, volt$. The electric field at the point $(1\, m, 0, 2\, m)$ in $volt/metre$ is
If on the concentric hollow spheres of radii $r$ and $R( > r)$ the charge $Q$ is distributed such that their surface densities are same then the potential at their common centre is
The equivalent capacitance of the combinatio shown in Figure is
Five point charges each having magnitude $'q'$ are placed at the corners of regular hexagon as shown in figure. Net electric field at the centre $'O'$ is $\vec E$ . To get net electric field at $'O'$ to be $6\vec E$ , charge placed on the remaining sixth corner should be