Three long concentric conducting cylindrical shells have radii R, 2R and 2√2 R. The inner and outer shells are connected together. The capacitance per unit length between the middle shell and the connected inner+outer shells is:
Select all that apply

Question

Three long concentric conducting cylindrical shells have radii R, 2R and 2√2 R. The inner and outer shells are connected together. The capacitance per unit length between the middle shell and the connected inner+outer shells is:

Select all that apply

G1 Physics · Accepted Answer

The middle shell forms two capacitors in parallel: with inner shell, C′₁=2π ε₀/ln2; with outer shell, ln[(2√2R)/(2R)]=ln√2=½ln2, so C′₂=4π ε₀/ln2. Sum =6π ε₀/ln2. Correct answer: B.