External electro-magneteic field acting on a wire

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Maniaks
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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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I understand that with a varying magnetic field we can induce current in the wire, which will either oppose or lead the existing current, but is possible to change the voltage?
 
So to , for example, increase the voltage, do I need an electrical field or magnetic field, or combination of both?
 
Maniaks said:
So to , for example, increase the voltage, do I need an electrical field or magnetic field, or combination of both?

If there is an electric field, the wire will feel it - the field is the gradient of the voltage.

For a magnetic field to generate an EMF it must be in motion wrt the wire ... just like any generator.