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Mathematical magnetic field
The α angle in this picture should be known. The solution under this condition is: in a circular area, the incidence of events is the largest, and there is only one possibility, that is, two points of MN are on the diameter of the circle, and all chords on the circle except the diameter are shorter than the diameter. The center of the uniform circular motion of ions in the magnetic field is on the vertical line passing through the middle vertical line of point M and diameter MN, that is, the O/ point in the figure. In the right triangle O/RM, the radius of the circle can be obtained by the right triangle function: r = r/sin α (1). The radius formula of uniform circular motion of ions in uniform magnetic field is: r=mV/(Bq), then v.

T = 2π m/(bq), and the movement time of ions in the magnetic field is t=2αT/(2π)=αT/π (2). Let the accelerating voltage of ions in the accelerating electric field be u, and according to the kinetic energy theorem: qu = 0.5mv2 = 0.5m [bqr/(msinα)] 2 = (bqr.