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External electro-magneteic field acting on a wire

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Hello, I am interested in knowing what happens ta wire trough which current is flowing, when an external magnetic, electrical or both , field is applied? Does the voltage or current change, can it be changed this way? Can you also provide some equations of this phenomenon, and also mix-induction, for example what happens to a wire which has an solenoid wrapped around it(leaving space between them), and if current flows trough the both of them or only one of them , what happens? This is only my personal interest in the topic, thank you in advance.

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