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Three cylindrical conducting shells of radii $a < b < c$ and of length $L \gg c$ are placed in a concentric configuration as shown. The middle shell is given a total charge $Q$, and both the inner and outer shells are grounded (connected by a thin wire to each other and to something at a potential of ``0''). Find:

a) The total charge on the inner shell, in terms of $a,b,c,L,Q$ and $k$.

b) The potential on the middle shell. In what direction does the field point in between $a$ and $b$ and in between $b$ and $c$?