A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports. Show that the capacitance of this spherical capacitor is given by `C = (4pi in_(0) r_(1) r_(2))/(r_(1) - r_(2))`,
Where `r_(1) and r_(2)` are radial of outer and inner spheres respectively.

Explanation

Radius of the outer shell =`r_(1)`
radius of the inner shell =`r_(2)`
The inner surface of the outer shell has charge +Q
the outer surface of the inner shell induced charge -Q.
potential difference between the two shells is given by,
`V=Q/(4piin_(0)r_(2))-Q/(4piin_(0)r_(1))`
where,
`in_(0)`=permitivity of free space
`V=Q/(4pi in_(0))[1/(r_(2))-1/(r_(1))]`
`=(Q(r_(1)-r_(2)))/(4piin_(0)r_(1)r_(2))`
capacitance of the given system is given by
`C=("Charge (Q)")/("Potential difference (V)")`
`=(4pi in_(0)r_(1)r_(2))/(r_(1)-r_(2))`
Henced proved.