$A$ small conducting sphere is hung by an insulating thread between the plates of a parallel plate capacitor as shown in the figure. The net force on the sphere is

'At the surface of a charged conductor,the electrostatic field must be normal to the surface at every point'. Explain.

Consider an initially neutral hollow conducting spherical shell with inner radius $r$ and outer radius $2r$. $A$ point charge $+Q$ is now placed inside the shell at a distance $r/2$ from the centre. The shell is then grounded by connecting the outer surface to the earth. $P$ is an external point at a distance $2r$ from the point charge $+Q$ on the line passing through the centre and the point charge $+Q$ as shown in the figure. The magnitude of the force on a test charge $+q$ placed at $P$ will be

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:

Two charged conducting spheres $S_1$ and $S_2$ of radii $8 \text{ cm}$ and $18 \text{ cm}$ are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on $S_1$ and $S_2$ spheres are $E_{S_1}$ and $E_{S_2}$ respectively. The value of $\frac{E_{S_1}}{E_{S_2}}$ is . . . . . . .

$A$ and $B$ are two concentric conducting spherical shells. $A$ is given a positive charge $+Q$ while $B$ is earthed. Then: