$A$ capacitor of capacitance $C$ is charged to a potential $V$. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is $......$

The capacitance $(C)$ of an isolated conducting sphere of radius $(a)$ is given by $4\pi \varepsilon_0 a$. If this sphere is enclosed by an earthed concentric sphere of radius $(b)$,and the ratio of the radii of the spheres is $\frac{b}{a} = n$,then the capacitance of such a system will be increased by a factor of:

Eight drops of mercury of equal radii and possessing equal charge combine to form a big drop. If the capacity of each drop is $C$,then the capacity of the big drop is: (in $C$)

The stratosphere acts as a conducting layer for the Earth. If the stratosphere extends up to $50 \ km$ from the Earth's surface,calculate the capacitance of the spherical capacitor formed between the Earth's surface and the stratosphere in $F$. Take the radius of the Earth as $6400 \ km$.

Consider a charged cylindrical capacitor. The magnitude of the electric field $\vec{E}$ in its annular region:

For the shown situation,in the steady state condition,the ratio of the charge stored in the first capacitor to the charge stored in the $n^{th}$ capacitor is: