If the energy stored in a spherical conductor having a charge of $12 \mu C$ is $6 \ J$,then the radius of the spherical conductor is (in $cm$)

$A$ spherical capacitor has an outer sphere of radius $5 \text{ cm}$ and an inner sphere of radius $2 \text{ cm}$. When the inner sphere is earthed,its capacity is $C_1$,and when the outer sphere is earthed,its capacity is $C_2$. Then $\frac{C_1}{C_2}$ 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:

If the circumference of a sphere is $3 \ m$,then the capacitance of the sphere in water is (dielectric constant of water = $80$) (in $pF$)

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 unit of electric permittivity is