A metallic sphere ' A ' isolated from ground is charged to $+50 \mu \mathrm{C}$. This sphere is brought in contact with other isolated metallic sphere ' $B$ ' of half the radius of sphere ' $A$ '. Then the charge on the two isolated spheres A \& B are in the ratio

A regular hexagon of side 10 cm has a charge $1 \mu \mathrm{C}$ at each of its vertices. The potential at the centre of hexagon is $\left[\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\right.$ SI unit $]$

Two charged particles each having charge ' $q$ ' and mass ' $m$ ' are held at rest while their separation is ' $r$ '. The speed of the particles when their separation is ' $\frac{\mathrm{r}}{2}$ ' will be ( $\varepsilon_0=$ permittivity of the medium)

A charge $+Q$ is placed at each of the diagonally opposite corners of a square. A charge -q is placed at each of the other diagonally opposite corners as shown. If the net electrical force on $+Q$ is zero, then $\frac{+Q}{-q}$ is equal to