When a dipole placed parallel to electric field is rotating through $\pi^c$, the work done is W. The work done in rotating the dipole through $\left(\dfrac{\pi}{3}\right)^c$ is
($\cos 0^\circ = 1$, $\cos 60^\circ = \dfrac{1}{2}$, $\cos 180^\circ = -1$)

The point charges $+q$, $-q$, $-q$, $+q$, $+Q$ and $-q$ are placed at the vertices of a regular hexagon ABCDEF as shown in the figure.

The electric field at the centre of the hexagon 'O' due to the five charges at A, B, C, D and F is thrice the electric field at centre 'O' due to charge $+Q$ at E alone. The value of Q is

Three point charges +q, +2q and +Q are placed at the vertices of an equilateral triangle. If the potential energy of the system of three charges is zero, the value of Q in terms of q is

Two point charges +e and +4e are kept at a distance 'd' units apart. Third point charge +q is placed between the two charges at a distance 'x' units from charge +e so as to be in equilibrium. The value of 'x' is