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

Charge $q$ is uniformly distributed over a thin half ring of radius $R$. The electric field at the centre of the ring is

Figures below show regular hexagons, with charges at the vertices, In which of the following cases the electric field at the centre is not zero.

A parallel plate capacitor with air between the plates has a capacitance of $9\ pF$. The separation between its plates is '$d$'. The space between the plates is now filled with two dielectrics. One of the dielectric has dielectric constant $K_1 = 6$ and thickness $\frac{d}{3}$ while the other one has dielectric constant $K_2 = 12$ and thickness $\frac{2d}{3}$. Capacitance of the capacitor is now........$pF$

What is the angle between the electric dipole moment and the electric field strength due  to it on the equatorial line.......$^o$

The four capacitors, each of $25\,\mu F$ are connected as shown in Fig. The $dc$ voltmeter reads $200\,V$. The charge on each plate of capacitor is