Final answer:
To express the magnitude of the magnetic field in terms of velocity and electron charge for an electron moving in a straight line, the net force must be zero. The Lorentz force equation indicates that either the magnetic field is zero or has no component perpendicular to the velocity of the electron, or it is counterbalanced by another force.
Step-by-step explanation:
To express the magnitude of the magnetic field in terms of the velocity v and the charge of the electron e, when an electron continues in a horizontal straight line, we can revisit the formula for the Lorentz force, which is given by F = qvB sin θ, where q is the charge, v is the velocity, B is the magnetic field, and θ is the angle between the velocity and the magnetic field. In the scenario where an electron moves in a straight line, the net force on it must be zero. Thus, for an electron moving horizontally without deflection, the magnetic field must be zero or directed in such a way that it does not exert a force on the electron. In a realistic scenario, such as the presence of Earth's magnetic field, it would be deflected unless an additional force, electric or magnetic, counterbalances the magnetic force.
If we were to consider a scenario where the electron is in a magnetic field perpendicular to its velocity, which causes the electron to move in a circle, we would use the equation F = qvB to describe the magnetic force causing circular motion. However, if the electron is not deflected, either the magnetic field has no component perpendicular to the velocity of the electron, or it is perfectly balanced by another force.