Source: High school physics (Chinese)
Problem Sets:
Problem
A beam of charged particles moves along a straight line.
- Describe the magnetic field produced by a proton beam moving away from you (into the page).
- 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.