Final answer:
The magnetic field required for an electron not to be deflected is determined by the equation B = E/v, and if the electric field is switched off, the electron moves in a circular path with radius r = mv/(qB).
Step-by-step explanation:
The student's question pertains to the behavior of an electron entering a region with a specific electric and magnetic field. To prevent the electron from being deflected as it passes through this region, the magnetic force and electric force must balance each other out. For an electron with velocity v, in an electric field E, the magnetic field B required to keep the electron undeflected can be determined using the equation Fm = Fe, where Fm = qvB (Lorentz force due to magnetic field) and Fe = qE (force due to electric field). Hence, B = E/v. If the electric field is then switched off, the electron would experience only the magnetic force, causing it to move in a circular path due to the centripetal force, and the radius r of this path can be calculated using the formula r = mv/(qB), where m is the mass of the electron, v its velocity, q its charge, and B the magnetic field.