Two charged spherical conductors of radius $R_{1}$ and $R_{2}$ are connected by a wire. Then the ratio of surface charge densities of the spheres $(\sigma_{1} / \sigma_{2})$ is:

Two spheres $A$ and $B$ are kept very near to each other. $A$ is negatively charged and $B$ is earthed. The true statement is:
$(A)$ Charge on $B$ is zero
$(B)$ Potential at $B$ is zero
$(C)$ Charge is uniformly distributed on $A$
$(D)$ Charge is non-uniformly distributed on $A$

Two conducting spheres of radii $20\, cm$ and $15\, cm$ are placed on insulating stands. Both are given an equal charge of $10\ \mu C$. When they are connected by a copper wire and then disconnected,which of the following is true?

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 . . . . . . .

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

$A$ neutral conducting solid sphere of radius $R$ has two spherical cavities of radius $a$ and $b$ as shown in the figure. The centre-to-centre distance between the two cavities is $c$. Charges $q_a$ and $q_b$ are placed at the centres of the cavities,respectively. The force between $q_a$ and $q_b$ is: