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Correct, Alternating m-field comes from alternating current.
Re 90 phase? Where electric strength and magnetic strength are always perpendicular, and always meet at zero. ie. where there is current there is always magnetism, vicer versa, see Maxwell's Laws.
Also important to think of the magnetic field as a fog (vector field). NOT lines (lines are just an easy way to quickly draw a field, like topographical lines to a mountain/valley.... they don't physically exist).
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