  We continue our study of 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) composite
solitons of vortex strings, domain walls and boojums in N=2 supersymmetric
Abelian gauge theories in four dimensions. In this work, we numerically confirm
that a boojum appearing at an end point of a string on a thick domain wall
behaves as a magnetic monopole with a fractional charge in three dimensions. We
introduce a "magnetic" scalar potential whose gradient gives magnetic fields.
Height of the magnetic potential has a geometrical meaning that is shape of the
domain wall. We find a semi-local extension of boojum which has an additional
size moduli at an end point of a semi-local string on the domain wall. Dyonic
solutions are also studied and we numerically confirm that the dyonic domain
wall becomes an electric capacitor storing opposite electric charges on its
skins. At the same time, the boojum becomes fractional dyon whose charge
density is proportional to ${\vec E} \cdot {\vec B}$. We also study dual
configurations with an infinite number of boojums and anti-boojums on parallel
lines and analyze the ability of domain walls to store magnetic charge as
magnetic capacitors. In understanding these phenomena, the magnetic scalar
potential plays an important role. We study the composite solitons from the
viewpoints of the Nambu-Goto and Dirac-Born-Infeld actions, and find the
semi-local BIon as the counterpart of the semi-local Boojum.
