Electron moving through a uniform magnetic field

[bioradical]

The Problem:
An electron moves with speed 9.00 105 m/s in a uniform magnetic field of 2.0 T, pointing south. At one instant, the electron experiences an upward magnetic force of 2.00 10-14 N. In what possible directions might the electron be moving at that instant? Give your answers as angles clockwise from south (from 0° to 360°), in increasing degrees.


The only equation needed should be F= lql * VBsin(theta)


I used the above equation and found the angle to be 3.98° counterclockwise of South. So my first answer was 360-3.98=356.02° (which was correct). My problem came with finding the angle at the second position. I initially thought that it would be 180-3.98, but, through guess work, I found that the correct answer is 180+3.98= 183.98. I'm not sure why this is right.

Can someone help me understand the concept behind the second possible position of the electron?

Thank you!

 

[tiny-tim]

Welcome to PF!

Hi bioradical! Welcome to PF!

So my first answer was 360-3.98=356.02° (which was correct). My problem came with finding the angle at the second position. I initially thought that it would be 180-3.98, but, through guess work, I found that the correct answer is 180+3.98= 183.98. I'm not sure why this is right.

Because what matters is sinθ.

sin(180º + θ), which was your first try, is minus sinθ (so the force would have to be down) …

but sin(180º - θ) is sinθ ​

 

[nlightner]

The reason why the correct answer is 180+3.98 is because the magnetic force acting on the electron is always perpendicular to both the direction of the electron's motion and the direction of the magnetic field. This means that the angle between the magnetic force and the direction of motion is always 90 degrees. Therefore, in order for the electron to experience an upward magnetic force, it must be moving in a direction that is perpendicular to the south direction (which is the direction of the magnetic field). This can be either 90 degrees clockwise or 90 degrees counterclockwise from the south direction, which corresponds to 180 degrees and 0 degrees, respectively. Since the electron is initially moving south, the second possible direction would be 180 degrees + the angle of 3.98 degrees counterclockwise from south, resulting in 180+3.98 = 183.98 degrees.