Three concentric conducting shells `A, B` and `C` of radii `a,b` and `c` are as shown in figure. A dielectric of dielectric constant `K` is filled between `A` and `B`. Find the capacitance between A and C.
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`E(r)=q/(4piepsilon_0Kr^2)` for `a,=rleb` `q/(4piepsilon_0r^2)` for `blerlec` using `dV=-intE.dr` the PD between `A` and `C` is `:. V=V_A-V_C=-int_a^bq/(4piepsilon_0Kr^2).dr-int_b^c q/(4piepsilon_0r^2)dr` `=q/(4piepsilon_0)[1/K(1/a-1/b)=(1/b-1/c)]=q/(4piepsilon_0)[((b-a))/(Kab)_((c-b))/(bc)]` `=q/(4piepsilon_0Kabc)[c(b-a)+Ka(c-b)]` `:.` The desired capacitance is `C=q/V=(4piepsilon_0Kabc)/(Ka(c-b)+c(b-a))`
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