# Three concentric spherical conductors are shown, Find equivalent capacitance b/w A and B

$\begin{array}{1 1}(A)\;\frac{4 \pi \in _0 bc}{c-b}+\frac{4 \pi \in _0 ab}{b-a} \\ (B)\;\frac{4 \pi \in _0 ac}{c-a} \\ (C)\; \frac{4 \pi \in _0 ac}{c-a}+4 \pi \in _0 c \\ (D)\;\frac{4 \pi \in _0 bc}{c-b}+\frac{4 \pi \in _0 abc}{ab+c(b-a)} \end{array}$

The innermost conductor is at zero potential (same as infinity)
Equivalent diagram can be drawn as :
$C_1= \large\frac{4 \pi \in _0 ab }{b-a}$
$C_2= 4 \pi \in _0 c$
$C_3= \large\frac{4 \pi \in _0 bc }{c-b}$
$C_{eq} = C_3 +\large\frac{C_1C_2}{C_1 +C_2}$
=> $\large\frac{4 \pi \in _0 bc}{c-b}+\frac{4 \pi \in _0 abc}{ab+c(b-a)}$
Hence D is the correct answer.
answered Jan 13, 2014 by