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Question

Three long concentric conducting cylindrical shells have radii R,2 R and 22 R. Inner and outer shells are connected to each other. The capacitance across middle and inner shells per unit length is:
  1. 13ϵ0ln2
  2. 6πϵ0ln2
  3. none of these
  4. πϵ02ln2

A
none of these
B
πϵ02ln2
C
13ϵ0ln2
D
6πϵ0ln2
Solution
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The equivalent structure is shown in figure. Here the capacitance between inner and middle cylinder is equal to equivalent capacitance when C1 and C2 are in parallel.
C1=2πϵ0ln(2RR)=2πϵ0ln2
C2=2πϵ0ln(22R2R)=4πϵ0ln2
Ceq=C1+C2=2πϵ0ln2+4πϵ0ln2=6πϵ0ln2
206422_126640_ans_46d75815247e45538c6d34b6e911bf81.png

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