Would a wire's magnetic field increase the net-B field?

[PhiowPhi]

From the following diagram:

When a wire is placed in a magnetic field $B$, and current starts to flow within that wire. It creates it's own magnetic field($B_w$). Will $B_w$ interact with the external field $B$? If it does, is the result of the interaction the Lorentz force?

Also from the direction of current the wire's magnetic field could oppose or support the external field, will that decrease/increase the total magnetic field, causing $\Delta$ ($\phi$) and will induced -$\epsilon$ to oppose the change?

Because in applications related to the Lorentz force I study(motors) the induced $\epsilon$ I am aware of, are from self-inductance of the wire, or the motion of the wire which causes the change in area. Not sure of anything else...

 

[mfb]

For all practical purposes, magnetic fields do not interact with each other. You can just add different contributions to find the total field at a point. They can influence other magnetic dipoles but that is a different type of interaction. The magnetic field of the wire is irrelevant if you want to study the effect of the outside magnetic field on the wire - as long as your wire does not influence the magnetic dipoles in the magnet.

 

[PhiowPhi]

I assumed that the field of the current-carrying wire would somehow increase/decrease the external magnetic field. Thanks for clearing out that misconception @mfb.

 

[Philip Wood]

I think that any confusion arises from there being two ways of 'understanding' the force on a current-carrying wire…

The 'Faraday picture' considers the RESULTANT of the wire's magnetic field and the external magnetic field. The resultant field lines are bunched on one side of the conductor and spaced out on the other, forming a swirly pattern. So far, so uncontroversial. But Faraday regarded the stretched and bunched-together field lines on one side of the wire as acting like a catapult and pushing 'sideways' on the current-carrying wire (as compared to the more spaced-out lines on the other side of the wire).

The modern approach is that the force arises by the action of the EXTERNAL field on the wire.

Confusion is caused when textbooks and teachers don't make a clear enough distinction between the approaches, so that the student gets a mixture of the two. One could argue that there's not a very strong case for teaching the catapult approach at all.