Final answer:
The trajectory of an electron with a given initial velocity entering a magnetic field will be circular, and one can calculate the force, acceleration, and radius of the trajectory using the provided formulas, assuming no other forces are acting on the electron.
Step-by-step explanation:
An electron entering a region of space with a magnetic field experiences a magnetic force calculated by the equation F = qvBsin(\theta), where 'q' is the charge of the electron, 'v' is its velocity, 'B' is the magnetic field, and '\theta' is the angle between the velocity and the magnetic field. Given the electron's initial velocity of 13,000 m/s due south and the magnetic field of 35.0 mT at 15.0 degrees east of north, we can find the force on the electron and the resulting acceleration. Since the force due to a magnetic field is always perpendicular to the velocity of a charged particle, the trajectory of the electron will be circular, assuming no other forces are acting on the electron.
The radius of the trajectory can be found using the equation r = mv/(qB), where 'm' is the mass of the electron. For an electron, m = 9.11 \times 10^{-31} kg and q = -1.60 \times 10^{-19} C. However, to provide a detailed answer, we need more information regarding the precise orientation of the magnetic field in relation to the electron's velocity.
If we do not have the exact angle at which the electron's velocity vector makes with the magnetic field, we cannot calculate the exact values for the force, acceleration, or radius of the trajectory.