Final answer:
The magnitude of the magnetic field in the region is approximately 0.051 T.
Step-by-step explanation:
The velocity of the electron is given as 3.70x103 m/s in the positive x direction, and the acceleration is given as 3.80x1012 m/s² in the positive z direction. Since the electric field is in the positive z direction, it will not affect the electron's velocity in the x direction. Therefore, only the magnetic field is responsible for the acceleration in the z direction.
The force acting on the electron is given by F=qvB, where F is the force, q is the charge of the electron, v is the velocity of the electron, and B is the magnetic field strength. In this case, the force is equal to the mass of the electron (m) multiplied by the acceleration (a) in the z direction, F = ma.
Setting these two equations equal to each other, ma = qvB, we can solve for the magnetic field strength, B = ma / (qv).
Substituting the given values, B = (3.80x1012 m/s²) / ((-1.60x10-19 C)(3.70x103 m/s)), we find that the magnitude of the magnetic field is approximately 0.051 T.