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Maxwell's equations connecting fields and sources apply in each inertial frame. When you transform to the proton's rest frame, you also see transformed sources (Helmholtz coils, etc).
But my question is how we justify the answer to this narrowly posed question
in terms of the E&M available in an introductory physics course. Where does
the electric field that the (assumed stationary) proton experiences come
from since there is no time varying magnetic flux from a uniform field?