# On the motion of a charged particle in a magnetic field

It's often said that a charged particle travelling in a straight line on a plane undergoes a circular trajectory whenever subjected to a uniform static magnetic field perpendicular to the plane.

But hold on. A charged particle in a circular motion acts much like a steady current on a loop. And this current produces a magnetic field which will point in the opposite direction of the external one. But in this way, the total net magnetic field diminishes. Consequently, the centripetal force $$\mathbf{F}_B=q\mathbf{v}\times\mathbf{B}_{\operatorname{net}}$$ will also diminish, and the radius of the Amperian loop will increase. At this point, the $$\mathbf{B}_{\operatorname{loop}}$$ field produced by this loop is much weaker, according to the formula $$\displaystyle B_{\operatorname{loop}}\approx \frac{\mu_0 I}{2\pi R}$$, and the external $$\mathbf{B}_{\operatorname{in}}$$ field is less weakened. The loop will therefore shrink again, and so on.

My point is that the orbit of this particle should oscillate continuously. Is this correct? An oscillating charge produces em waves by the way... are these em waves strong enough to complicate the scenario even further?

• Your question boils down to "does a point charge experience a force from the fields it creates?", for which the answer is "no" in an introductory class and "it's complicated" in an upper-level E&M class. See this question and references therein for further discussion. Jun 28, 2022 at 20:57