Two metal spheres of radius $R$ and $3R$ have the same surface charge density $\sigma$. If they are brought in contact and then separated, the surface charge density on the smaller and bigger sphere becomes $\sigma_1$ and $\sigma_2$, respectively. The ratio $\frac{\sigma_1}{\sigma_2}$ is:

If two conducting spheres are separately charged and then brought in contact,which of the following statements is true?

When a conducting soap bubble is negatively charged,then:

Two conducting spheres $A$ and $B$ have radii $1 \, mm$ and $2 \, mm$ respectively and are charged. They are placed at a distance of $5 \, cm$. When they are connected by a conducting wire,the ratio of the electric field intensities on their surfaces at equilibrium is:

$A$ charge of $Q$ coulomb is placed on a solid piece of metal of irregular shape. The charge will distribute itself:

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