Capacity of a condenser whose plates are circular arcs

We find an asymptotic formula for the conformal capacity of a plane condenser both plate of which are concentric circular arcs as the distance between them vanishes. This result generalizes the formula for the capacity of parallel linear plate condenser found by Simonenko and Chekulaeva in 1972 and sheds light on the problem of finding an asymptotic formula for the capacity of condenser whose plates are arbitrary parallel curves. This problem was posed and partially solved by R. K\"{u}hnau in 1998.