A filamentary wire carries a current along the positive z-axis in the presence of a constant magnetic

Question:

A filamentary wire carries a current along the positive z-axis in the presence of a constant magnetic field B = B₀ x̂ + B'ẑ.

(a) Find the straight line in space along which the magnitude of the total magnetic field has an absolute minimum.
(b) Find the frequency of small oscillations in the vicinity of the line found above for an atom (mass M) trapped near the line found in part (a) by the virtue of the fact that its magnetic dipole moment m
remains anti-parallel to the local magnetic field direction at all times.
(c) How does the situation change if B' = 0?

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