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.

A spherical capacitor consists of two concentric spherical conductors,

1.	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.
Answer» 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.

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