a. Two spheres have radii `a` and `b` and their centres are at a distance d apart. Show that the capacitance of this system is
`C=(4piepsilon_0)/(1/a+1/b+-2/d)`
provided that `d` is large compared with `a` and `b`.
b. Show that as `d` approaches infinity the above result reduces to that of two islotated spheres inseries.

Explanation

a. `PD, V=V_1+V_2`

`=1/(4piepsilon_0)[(q/a-q/d)-((-q)/b+q/d)`
`:. C=q/V-(4piepsilon_0)/(1/a+1/b-2/d)`
If `-q` is given to first shere and `+q` to second sphere, then
`C=(4piepsilon_0)/(1/a+1/b+2/d)`
b. If `drarroo`, then `C=(4piepsilon_0)/(1/a+1/b)=((4piepsilon_0)(ab))/(a+b)`
in series, `C_(net)=(C_1C_2)/(C_1+C_2)=((4piepsilon_0a)(4piepsilon_0b))/((4piepsilon_0a)+(4piepsilon_0b))=(((4piepsilon_0)ab)/(a+b))`