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Bose-Einstein Condensation (BEC) was introduced by Einstein 1925. It took 70 years to con rm BEC by experiments. BEC creates a suitable environment to observe macroscopic-quantum behavior. Condensates consist of ultracold atoms allow physicists to create super uids and also they allow to manipulate these quantum structures easily. One of the main tool needed to manipulate these structures is synthetic magnetic eld. Under the light of these experimental achievements we studied the angular momentum transfer in the N-body systems. First of all, to develop physical intuition, we solved 2-body problem. This problem can be de ned as: The system consist of two particles and con ned in a ring. Particles interact with each other and charged one coupled to the magnetic eld. We used two approaches to solve the system and compared these approaches in the small limit of inter-particle interaction. Finally, we studied N-body systems and vortex transfer in the two-component super uid mixtures via Gross-Pitaevski equation and Bogoulibov equations. We observed that for various parameters neutral-neutral mixtures do not possess vortex transfer, yet charged-neutral mixtures coupled to the magnetic eld experience vortex transfer.