An electron is traveling east with an instantaneous velocity of 3.3 × 10⁵ m/s when it enters a uniform magnetic field of 0.25 T that points X degrees north of east. Take east as to the right of the paper and north as toward the top of the paper, i.e., both in the plane of the paper.) If the magnitude of the force on the electron is 5.5 × 10^-15 N, then calculate the angle X and whether the electron moves up out of or down into the plane of the page, or otherwise.

Question

Quizplus · Accepted Answer

Using the right hand rule, we can determine that the force on the electron is directed downward into the plane of the paper (perpendicular to both the magnetic field and velocity). Since the electron is negatively charged, its acceleration is in the opposite direction of the force, which means it curves downward into the plane of the paper. Therefore, the angle X must be less than 90 degrees (i.e. pointing downward) in order for the force to push the electron downward into the plane of the paper. Solving for X using the formula for the magnetic force on a charged particle, we get:

F = qvBsin(X)
5.5 × 10^-15 N = (1.6 × 10^-19 C)(3.3 × 10^5 m/s)(0.25 T)sin(X)
sin(X) = 0.25
X = 14.5 degrees

Since X is less than 90 degrees and the force direction is downward, the electron must be moving downward into the plane of the paper. Therefore, the best choice is C: 25° and down into the page.

An Electron Is Traveling East with an Instantaneous Velocity of 3.3