Trace of cathode ray in changing magnetic field.

[Samson4]

I know that cathode rays follow a helical pattern if they enter a uniform magnetic field at an angle less than 90 degrees. This leaves me with two questions.
1. If the cathode ray described above, hit a phosphor coated screen, would it show only 1 spot or a circle?

2. If the magnetic field was constantly changing in strength, would the spot trace a path of spiral, concentric circles or some other shape?

 

[BvU]

1. The beam follows a helical pattern indeed, so the intersection with a plane is always just one single point (ignoring the beam size).

2. Helix radius is proportional to 1/B . All other things remaining the same you get the spiral. (screen $\bot$ Helix axis)

 

[Samson4]

Thank you so much.

 

[Samson4]

If the cathode ray is aimed through a coil; and the coil is energized with ac, how will the electrons behave as they approach the varying magnetic field generated by the coil?

I think the electrons will form a current loop with increasing diameter as it approaches the coil. I also think the diameter of the loop will depend on the strength of the magnetic field. The direction of spin will correlate with the polarity of the field. Is this all wrong?

 

[BvU]

If you aim properly, the magnetic field is parallel with the beam, so nothing happens to the electrons .

If you mean something else, perhaps you can post a drawing of the situation ?

 

[Samson4]

Oh no, these electrons are killing me. That's exactly what I thought until I "learned" more and convinced myself otherwise.

How come the varying magnetic field won't effect the electron beam? I thought a uniform time-varying magnetic field induces an electric field by Faraday's law. If an electron at rest will spiral in a time varying field, why won't one moving towards the field also spiral? On another view of the same situation; if the coil is far enough away or small enough, wouldn't the electrons experience a force in the direction of the nonuniform magnetic field?

If I'm not making since I will make a drawing after work. I really appreciate your help.