# Why is there no B-field parallel force on an electron orbiting a magnetic field line?

If an orbiting electron creates a toroidal magnetic field like a ring of current does, and this field is oriented opposite to the magnetic field line the electron is orbiting, then why is the electron not repelled by the applied field that it orbits (driven along the field line) like 2 end to end bar magnets of opposite polarity?

• @AaronStevens That's true, but that's not the reason for the phenomenon the question is asking about. You could have a uniformly charged ring rotating in a constant normal magnetic field (making the problem magnetostatic), and the question would be the same. – Buzz Jun 6 at 4:14
• electrons are quantum mechanical entities, and interact with macroscopic magnetic fields as single charge particles. If you are thinking of orbitals in atoms, then there exist corrections due to magnetic field interactions hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydfin.html – anna v Jun 6 at 4:17
• @Buzz Then I guess it depends on if the externally applied field is uniform or not. – Aaron Stevens Jun 6 at 4:18
• @annav A moving point charge will generate a magnetic field. It is more complicated than the field of a steady current. However, the qualitative problem the question is asking about still exists when there is just the field of a single charge in circular motion. – Buzz Jun 6 at 4:26
• @Matthew Is the externally applied field uniform? – Aaron Stevens Jun 6 at 4:27

If the applied magnetic field is uniform then there cannot be a net force on the current loop. This is because the magnetic force $$\text d\mathbf F$$ experienced by a small part of the loop of length $$\text dl$$ of current $$I$$ is given by $$\text d\mathbf F=I\text d\mathbf l\times\mathbf B$$
If we integrate this around the loop for a uniform field you will find that the net force is $$0$$ (and the loop will be either under stretching or compressive forces). So for the example given in the comments, a ring of current inside a solenoid would not experience a net force in the direction of the solenoid (it could experience a torque though)