A line from a magnetic white dwarf

Adapted from IOAA 2023 (Katowice), theory problem Q2. We have restated it in our own words and kept the original data. The solution was last checked on 20 October 2026.

An emission line of wavelength 600 nm is seen in the spectrum of a white dwarf. Assume that it comes from free electrons, moving much slower than light, that circle in the star's magnetic field.

(a) Find the magnetic flux density $B$ of the field.

(b) Estimate the wavelength of another line whose discovery would confirm that the lines come from the particles of a plasma circling in the field.

AnswerThe field is about $2\times {10}^4$ T, hundreds of millions of times stronger than Earth's, and a line from protons should appear near 1.1 mm.