Final answer:
The gauge potential of an electron in a uniform magnetic field is non-zero and depends on the strength and direction of the magnetic field.
Step-by-step explanation:
Gauge potential is a mathematical representation of the electromagnetic potential in a given system. In the case of an electron in a uniform magnetic field, the gauge potential is non-zero. The gauge potential is related to the magnetic vector potential, which describes the magnetic field in terms of a vector quantity. The magnitude and direction of the gauge potential depend on the strength and direction of the magnetic field.