Why is the force on a current carrying loop non-zero?

Question

Suppose I have a closed circular loop kept on a horizontal plane with current $i$ flowing through it in a clockwise direction. A magnetic field $B$ is created by bringing a bar magnet with north pole facing the loop. If I consider a small element $dl$ on the loop, the force acting on it due to the magnetic field would be $idlB$ in the outward direction. Similarly, all the small elements on the loop will experience a force in the outward direction which will eventually cancel out, and the resultant will be $0$.
Due to the clockwise current in the loop, a magnetic field will be generated which will make the loop act as a bar magnet with north pole facing outwards. Shouldn't the north poles(one which is created due to current and other due to bar magnet creating magnetic field $B$) repel each other? Wouldn't this make the net force on the loop non-zero? (assuming gravity-free space and no normal reaction forces). So why do we say that net force on a current-carrying loop is zero?

Answer 1

(a) What you are forgetting is that the field beyond the North Pole of a bar magnet is not parallel to the magnet's longitudinal axis of symmetry, but has a component directed outwards from this axis. The magnetic field lines splay out! [The exception is along the axis of symmetry itself.]

So the motor effect force on your loop element, $dl$, will have a component parallel to the (common) axis of the magnet and loop. So we do have agreement with the loop experiencing a force as would another magnet. The force on the loop depends on the actual magnet's field being non-uniform. [In a uniform magnetic field the loop would experience no net force but perhaps (depending on orientation) a torque.]

(b) "Due to the clockwise current in the loop, a magnetic field will be generated which will make the loop act as a bar magnet with north pole facing outwards." I don't know what you mean by 'facing outwards' The North pole of the loop is the face of the loop further from the viewer of your screen. This is because the magnetic field lines are coming out of this face.