Calculating Vectors (in Joules) of an electromagnet

[Blackhawk4560]

Good afternoon,

Question: Say I have an electromagnet at a 45 degree incline from an electron beam. This electromagnet is exerting 0.75 Tesla on the beam. How can I calculate the vector that the electromagnet will exert on a particle? Note, this is for my own curiosity, not for any homework assignment- Therefore, feel free to make up numbers if needed...

I hope I explained well enough, if not, check out the attached image~

Thank you in advance!

 

[mfb]

How can I calculate the vector that the electromagnet will exert on a particle?

The force vector?
This is just the Lorentz force: $\vec F = q \vec v \times \vec B$ with the cross-product. It is orthogonal to both the magnetic field and the particle motion at the same time.

If the deflection is significant, v and therefore the force will change while the electrons are passing the magnet.

 

[Blackhawk4560]

Ohhhh I've worked with Lorentz prior, I totally forgot that they have a vector form... Anyway, so secondary question: How do magnets speed up electrons, like we see in CRT's and medical equipment? Wouldn't any magnet automatically slam an electron beam into the wall in order to be perpendicular? Again, hope I worded that in a pseudo-coherent manor...

Thanks again! The help is certainly appreciated!

 

[mfb]

They don't. Acceleration is done via electric fields.

Time-dependent magnetic fields can do that as well (as they induce electric fields), but that is rarely used for electron beams.

 

[Blackhawk4560]

Ohhhh that makes sense- I am ashamed to say how long I spent with the right hand rule trying to get them to add up! Anyway, just to make sure I'm on the same page, Is it just a series of increasingly powerful/ timed anodes to pull the beam forward? I would figure as much... See the attached diagram

Thank you again for the support!

 

[mfb]

A single anode can be sufficient. That is the basic idea of CRT tubes, conventional x-ray production and so on.

The energy is limited by the voltage, so for very high energies (more thana few MeV) other techniques have to be used. Switching the voltages of the (multiple) electrodes is one approach and leads to the concept of a linac.

 

[Blackhawk4560]

Beautiful- Thank you again for your time!