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How do the two fields interact to give the combined field, do they superpose like in waves? And how does this field cause the force on the conductor?

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Magnetic fields indeed simply combine via superposition - like in waves. The potential energy of magnetism is $V=-\frac{1}{2}\mu\cdot B$ where $\mu$ is the magnetic moment (vector) of the, in this case, conductor and $B$ is the magnetic field strength (vector) and the dot represents the scalar product. The magnetic moment depends in general on the imposing magnetic field (for para- or diamagnetism) or in the current in the conductor. The force is then simply the negative gradient of the potential, i.e., $F=-\nabla V=\frac{1}{2}\nabla(\mu\cdot B)$. The gradient points into the direction of the steepest slope of the function it acts on, in this case the potential $V$. As $V$ consists of a dot product, we have on the side where the vector arrows point into the same direction a positive value and on the other side a negative value. (On the top and bottom the arrows are perpendicular to each other and the product therefore vanishes at these points and we have a smooth change between zero and the largest value.) The gradient now points into the direction where we have the larger value (where the vector arrows are parallel and not anti-parallel) but since we have for the force the negative gradient the resulting force points outwards of the magnet in your sketch.

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