The Biot-Savart law as applied to a single point charge is described to be:
as retrieved from here.
Now we consider the following system of 2 similar charged particles:
By this definition, the B component from Biot-Savart law points in the z-direction (into or out of the page).
But then, the actual force F which is experienced by the object is said to be normal to B.
But this only puts the resultant force and acceleration experienced by the object back into the xy-plane without z-component, won't it?
So, the two objects' motion will stay in the same xy-plane forever, without straying into the z-component. Is this the right interpretation for the magnetic effect?