5-02-09 Capacitance of Spherical Shells

I think capacitance is
C=4Πε₀ab/b-a

if a charge q is given to the inner spherical conductor, it spreads over the outer surface of it and a charge -q appears on the inner surface of the shell. The electric field is produced onnly between the two.

the potential difference between the two is given by

v=q/4Πε (1/a -1/b)

using c=q/v we get

c=q/4Πε(ab/b-a)

1) we take a gaussian surface in between the two spheres.

we get , E = kQ/r²

2) dV =-E.dr

we find potential by integrting between a to b.

V= kQ(1/a-1/b)

3) then C=Q/V.

is this wat you wanted..... ??

if so, then [1] [this wasnt like QOD]

or else [3]

dV=-∫Q/4πε₀r²dr

V=Q/4πε₀[1/a-1/b]

C=Q/V=4πε₀[1/a-1/b]

is my soln right or wrong???????????????????????????????

[3]