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The vacuum structure of N=2 (and N=4) SUSY Yang-Mills theory is analyzed indetail by considering the effective potential for constant background scalar-magnetic fields within different approximations. We compare the one-loopapproximation with- or without instanton improved effective coupling with theone-loop result in the dual desription. For N=2 we find that non-perturbativemonopole degrees of freedom remove the non-trivial minima present in the(improved) one-loop potential in the strong-coupling regime. The combination ofYang-Mills and dual desription leads to a self-consistent effective potentialover the full range of background fields.Comment: 15 pages, Revtex, 3 figures, References added, section two shortened,  some minor remarks and corrections adde

SU(2) Yang-Mills theory with extended supersymmetry in a background magnetic field