Magnetic Field of Moving Charged-Particle Beams

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Magnetism Beginner Magnetic Field of Current

Source: High school physics (Chinese)

Problem Sets:

magnetic field

Problem

A beam of charged particles moves along a straight line.

  1. Describe the magnetic field produced by a proton beam moving away from you (into the page).
  2. Describe the magnetic field produced by an electron beam moving toward you (out of the page). Sketch both fields.

Both beams produce the same magnetic field: concentric circles around the beam axis, directed clockwise when viewed from the observer's side (because in both cases the conventional current points away from the observer).

A line of moving charge is equivalent to a current $I$, which produces concentric circular field lines around the line of motion. The direction is given by the right-hand rule: thumb along conventional current $\vec{I}$, fingers curl in the direction of $\vec{B}$.

Proton beam moving away from you: Positive charges moving away $\Rightarrow$ conventional current $\vec{I}$ points away from you (into the page). Pointing the right thumb into the page, the fingers curl clockwise as viewed from your side. So $\vec{B}$ lines are concentric circles around the beam, going clockwise from your viewpoint.

Electron beam moving toward you: Negative charges moving toward you $\Rightarrow$ conventional current $\vec{I}$ points away from you (into the page) — same direction as case 1. Hence the magnetic field pattern is identical: concentric circles going clockwise around the beam as viewed from your side.