Trajectory of a particle in a field

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Drawing the trajectory of a charged particle in a circular field.
The field is constant between two radii. The particle is shot from the center in radial direction, with a given angle. It enters in the field, follows a circular arc while it is in the field, and exits the field at external radius, being deflacted a given angle. The problem is to draw this trajectory for any values of the internal and external radii, the initial angle, and the deflaction. This creates an interesting geometric problem which Tikz can solve nicely.

Source Code

The diagram shows some "helping" points used to build the final trajectory (in blue), in order to make clearer the building procedure.