A path that curves more sharply (e-)?

[jayayo]

Homework Statement

Electron A is fired horizontally with speed 1.00 Mm/s into a region where a vertical magnetic field exists. Electron B is fired along the same path with speed 2.00 Mm/s. Which electron has a path that curves more sharply?
A does.
B does.
The particles follow the same curved path.
The particles continue to go straight.

Homework Equations

F=qv x B

The Attempt at a Solution

q and B for both are the same. The only difference is force and velocity. Because A has a smaller velocity, the force will be smaller; thus, the curve will be less sharp.

However, this site says A curves more sharply. Site:
http://physcourses.lums.edu.pk/wp-content/uploads/2014/01/Final-Exam.pdf

I'm not understanding why...

Thank you!

 

[jayayo]

I got from here (page 4 bottom), an equation for x (the distance reflected from its original path)
http://sun.iwu.edu/~gspaldin/B_deflection_Lab.pdf

Is this why? Does Vacc mean velocity??

Thanks anyone for any clarification..!

 

[berkeman]

I got from here (page 4 bottom), an equation for x (the distance reflected from its original path)
http://sun.iwu.edu/~gspaldin/B_deflection_Lab.pdf

Is this why? Does Vacc mean velocity??

Thanks anyone for any clarification..!

No, see the bottom of page 37 of the PDF. Vacc is the accelerating voltage applied to the electrons.

To solve this problem, work out the "Lamor Radius" of the circular motion of the electrons around the magnetic field lines. What are the equations of uniform circular motion in terms of velocity and centripital force?

If you have trouble working it out, look up "Gyroradius" at wikipedia...

 

[jayayo]

No, see the bottom of page 37 of the PDF. Vacc is the accelerating voltage applied to the electrons.

To solve this problem, work out the "Lamor Radius" of the circular motion of the electrons around the magnetic field lines. What are the equations of uniform circular motion in terms of velocity and centripital force?

If you have trouble working it out, look up "Gyroradius" at wikipedia...

wow stupid oversight on my part. Thanks so much!

 

[HalfLostAndSearching]

I would say that the answer to this question is not completely clear and may depend on specific details of the situation. In general, the path of a charged particle in a magnetic field will depend on the strength of the magnetic field, the velocity of the particle, and the charge of the particle. So, in this case, we need more information about the strength of the magnetic field and the charge of the particles to determine which one will curve more sharply.

However, based on the information given, it is likely that electron A will curve more sharply because it has a smaller velocity. This means that the force on electron A will be smaller, and therefore its path will be more curved. This is because the force on a charged particle in a magnetic field is proportional to both the velocity and the strength of the magnetic field. So, a smaller velocity will result in a smaller force and a more curved path.

Additionally, the equation F=qv x B only gives the magnitude of the force, not the direction. So, even though the force on both particles may be the same, the direction of the force may be different, leading to different paths.

Overall, without more information, it is difficult to determine which particle will have a more sharply curved path. However, based on the given information, it is likely that electron A will have a more sharply curved path due to its smaller velocity.