The vectors of the magnetic field around a long, straight, current-carrying wire are:

Divide the long wire in small segments. The field due to one segment can be found from Biot- Savart law.

dB=(uo/4pi) Idlxr/r^3. In this expression if we take vector r perpendicular to current element , the cross product in the expression shows that the direction of B is perpendicular to vector r and from symmetry it can be said that field line is circular around the wire segment. This is true for all segment ,because in infinitely long wire all segments are equivalent . Thus, magnetic field lines are concentric around a long straight wire.

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