$A$ metallic sphere $A$ isolated from the ground is charged to $+50 \mu C$. This sphere is brought into contact with another isolated metallic sphere $B$ of half the radius of sphere $A$. Then the charge on the two isolated spheres $A$ and $B$ are in the ratio:

$A$ conducting sphere of radius $10\, cm$ is charged with $10\,\mu C$. Another uncharged sphere of radius $20\, cm$ is allowed to touch it for some time. After the spheres are separated,the ratio of the surface charge densities on the spheres will be:

Conduction electrons are almost uniformly distributed within a conducting plate. When placed in an electrostatic field $\overrightarrow{E}$,the electric field within the plate

An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in the figure. If it is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the outer surface carries a uniform charge density $\sigma'$,if the outer surface of the shell is earthed,then identify the correct statement$(s)$.

Two charged spherical conductors of radii $R_1$ and $R_2$ are connected by a wire. The ratio of surface charge densities of the spheres $\sigma_1/\sigma_2$ will be

Explain the construction of a Van de Graaff generator with a diagram and describe its uses.