Force acting on a current carrying conductor within a magnetic field

[sss]

I am new to this forum, and this is my first post. Please bear with me if my query has any inaccuracies.

In the attached figure, a coil is wrapped around the central arm of a flat H-shaped thin metallic plate (such as iron). DC current flows through the coil and magnetizes the arm. At the same time, DC current also flows from another source through the plate as shown in the figure. Within the central arm, the directions of flow of the magnetic flux and current are perpendicular to each other.

If B is the magnetic flux density, L is the length along which the current I flows through the arm, does the plate experience a force F according to the equation F = B I L ?

I am asking this question because generally when we read about force acting on a current carrying conductor in a magnetic field, the magnetic field is understood to be external to the conductor. In this case, it is not. Hence, the query.

 

[Delta2]

Yes i think there would be a BiL force and it will be perpendicular to the plane of the page.

But i don't understand why you think that the magnetic field is not external in this case. Because it runs through the interior of the H-shaped conductor? But this happens for all external magnetic fields, they can penetrate through any conductor.
BiL force will not happen if the external magnetic field doesn't penetrate inside the conductor where the charge carriers flow and makeup the current i.

 

[anuttarasammyak]

Yes i think there would be a BiL force and it will be perpendicular to the plane of the page.

I would add that the coil gets reaction force of the opposite direction. The conductor sheet and wrapping coil repulse and no perpendicular motion would take place in total apparatus, if no rupture occurs.