$12 \mu C$ and $6 \mu C$ charges are given to two conducting plates having the same cross-sectional area and placed face to face close to each other as shown in the figure. The resulting charge distribution in $\mu C$ on surfaces $A, B, C$ and $D$ are respectively,

Two isolated metallic solid spheres of radii $R$ and $2R$ are charged such that both have the same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $\sigma^{\prime}$,then the ratio $\frac{\sigma^{\prime}}{\sigma}$ is:

$A$ spherical metal shell $A$ of radius $R_A$ and a solid metal sphere $B$ of radius $R_B < R_A$ are kept far apart and each is given charge $+Q$. Now they are connected by a thin metal wire. Then:
$(A)$ $E_A^{\text{inside}} = 0$
$(B)$ $Q_A > Q_B$
$(C)$ $\frac{\sigma_A}{\sigma_B} = \frac{R_B}{R_A}$
$(D)$ $E_A^{\text{on surface}} < E_B^{\text{on surface}}$

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:

Consider a metal sphere of radius $R$ that is cut into two parts along a plane whose minimum distance from the sphere's centre is $h$. The sphere is uniformly charged with a total electric charge $Q$. The minimum force necessary to hold the two parts of the sphere together is:

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