Three long concentric conducting cylindrical shells have radii R,2R and 2√2R. Inner and outer shells are connected to each other. The capacitance across middle and inner shells per unit length is:
13ϵ0ln2
6πϵ0ln2
noneofthese
πϵ02ln2
A
noneofthese
B
πϵ02ln2
C
13ϵ0ln2
D
6πϵ0ln2
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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(2√2R2R)=4πϵ0ln2 Ceq=C1+C2=2πϵ0ln2+4πϵ0ln2=6πϵ0ln2
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