Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

The radius of a soap bubble whose potential is $16\,V$ is doubled. The new potential of the bubble will be.....$V$

Consider a sphere of radius $R$ with uniform charge density and total charge $Q$. The electrostatic potential distribution inside the sphere is given by $\theta_{(r)}=\frac{Q}{4 \pi \varepsilon_{0} R}\left(a+b(r / R)^{C}\right)$. Note that the zero of potential is at infinity. The values of $(a, b, c)$ are

Twenty seven drops of water of the same size are equally and similarly charged. They are then united to form a bigger drop. By what factor will the electrical potential changes.........$times$

A thin spherical conducting shell of radius $R$ has a charge $q$. Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at a point $p$ at distance $\frac{R}{2}$ from the centre of the shell is

Three concentric spherical metallic shells $X , Y$ and $Z$ of radius $a , b$ and c respectively $[ a < b < c ]$ have surface charge densities $\sigma,-\sigma$ and $\sigma$, respectively. The shells $X$ and $Z$ are at same potential. If the radii of $X$ and $Y$ are $2\,cm$ and $3\,cm$, respectively.The radius of shell $Z$ is $......cm$.