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

The Earth is assumed to be a charged conducting sphere having volume $V$ and surface area $A$. The capacitance of the Earth in free space is

The capacitance of an isolated sphere of radius $r_1$ is increased by $5$ times,when it is enclosed by an earthed concentric sphere of radius $r_2$. The ratio of their radii is

$A$ conductor is connected to a battery of $5\, V$. It acquires a charge of $50\ \mu C$. Calculate the capacitance of the conductor in $\mu F$.

The magnitude of electric field $E$ in the annular region of a charged cylindrical capacitor:

$A$ 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.