$A$ drop of capacitance $1 \ \mu F$ is divided into $8$ identical drops. The capacitance of each small drop is .... $\mu F$.

$A$ sphere of $4\, cm$ radius is suspended within a hollow sphere of $6\, cm$ radius. The inner sphere is charged to a potential of $3\, e.s.u.$ and the outer sphere is earthed. The charge on the inner sphere is.....$e.s.u.$

The capacitance of a spherical condenser is $1\,\mu F$. If the spacing between the two spheres is $1\,mm$,then the radius of the outer sphere is

$A$ spherical capacitor has an inner sphere of radius $12 \;cm$ and an outer sphere of radius $13 \;cm$. The outer sphere is earthed and the inner sphere is given a charge of $2.5 \;\mu C$. The space between the concentric spheres is filled with a liquid of dielectric constant $32$.
$(a)$ Determine the capacitance of the capacitor.
$(b)$ What is the potential of the inner sphere?
$(c)$ Compare the capacitance of this capacitor with that of an isolated sphere of radius $12 \;cm$. Explain why the latter is much smaller.

$A$ spherical condenser has inner and outer spheres of radii $a$ and $b$ respectively. The space between the two is filled with air. The difference between the capacities of two condensers formed when the outer sphere is earthed and when the inner sphere is earthed will be:

Capacitance of an isolated conducting sphere of radius $R_{1}$ becomes $n$ times when it is enclosed by a concentric conducting sphere of radius $R_{2}$ connected to earth. The ratio of their radii $\left(\frac{R_{2}}{R_{1}}\right)$ is: