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Statement

10.1.29∗. In strong magnetic fields, an electron moves along a helical line "wound" onto the magnetic field line. Prove that in the case when the radius of the helix is so small that the field inside it can be considered homogeneous, the product of the square of the radius of the helix and the induction of the magnetic field does not change.

For problem $10.1.29$

Solution

The proof here will be very brief, referring to the solution of problem 10.1.24, the value of the invariant for the spiral trajectory was derived.:

Where is the distance from the side circle to the axis of the main orbit, with this equality inevitably follows:

Answer

Q.E.D.