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One answer to this is that there is no answer; it is just a fundamental property of, or equivalently part of the definition of, a magnetic field that it produces a force on a charged particle perpendicular to both the field and the particle's velocity. (Though the existence and properties of the magnetic field can be derived from the electric field in relativity.)

However, if you're so inclined, this can also be seen by an argument from symmetry and energy conservation. Let's say there is a magnetic field parallel to a current flow, and let's say there's a force on the flowing particles which can be predicted mathematically from the field. Which direction is it in? By symmetry it must be either with or against the current. All directions perpendicular to the current and field are the same; there's no physical law that could choose between them. This also means the field is either doing work on the current or having work done on it.

So which is it? Now consider how that magnetic field is generated. It must be generated by another current flowing perpendicular to the first one. Let the two currents be the same. Now we see that by a reflection and a rotation the two currents are interchangeable. So, if each generates a force on the other, either both the currents are doing work or both are having work done on them; either way this violates energy conservation and cannot be.

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Q: Why is magnetic force 0 if angle between current flow and magnetic field is 0?
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