Understanding the Relationship Between Magnetic Field and Current

[Gear2d]

I need some help with magnetic field and current. If have a magnetic field that is into the page:

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and say I pull a circular wire out of it which would current go to decrease the magnetic field? I am guessing that a clockwise would decrease the field where the magnetic field is into the page, and a counterclockwise current would increase the filed if the magnetic field were OUT of the page. But I cannot seem to find the logic as to why the current goes the way it does.

 

[Defennder]

When the magnetic field into the page is decreasing, you should expect a "counter" effect caused by the induced emf and resulting current to generate a magnetic field to oppose the change. This opposition comes in the form of reinforcing the weakening magnetic field into the page, so you should expect the generated magnetic field to go into the page and the corresponding current flow to be in the clockwise direction to generate that magnetic field.