An electron enters a region of uniform perpendicular fields. It is observed that the velocity of the electron is unaffected. A possible explanation is:
A) is parallel to and has magnitude E/B
B) is parallel to
C) is perpendicular to both and has magnitude B/E
D) is perpendicular to both and has magnitude E/B
E) the given situation is impossible

Question

An electron enters a region of uniform perpendicular  fields. It is observed that the velocity  of the electron is unaffected. A possible explanation is:
A) is parallel to and has magnitude E/B 
B) is parallel to 
C) is perpendicular to both and has magnitude B/E 
D) is perpendicular to both and has magnitude E/B 
E) the given situation is impossible

Quizplus · Accepted Answer

When a charged particle moves perpendicular to a uniform magnetic field, it experiences a force perpendicular to both its velocity and the field direction. This force causes the particle to move in a circular path with a constant speed, known as the cyclotron frequency. The radius of the path is proportional to the particle's momentum, which is determined by its velocity. Therefore, if the velocity is unaffected by the magnetic field, the only way for the particle to move in a straight line is if there is an electric field present that exactly cancels the magnetic force, which is perpendicular to both the velocity and the field direction. This requires the electric field to be perpendicular to the magnetic field, with a magnitude of E/B. Thus, choice D is the correct answer.

An Electron Enters a Region of Uniform Perpendicular Fields