Electron Radius in a Bending Magnet

In summary, the problem involves finding the radius of the path of 15 MeV electrons in a .7 tesla magnetic field. The equation used is r = mV/Bq, but this equation is only valid for non-relativistic electrons. The correct equation for relativistic electrons should be used instead.
  • #1
mh1551
3
0
Problem:

15 MeV electrons enter a bending magnet with a magnetic field of .7 tesla. What is the radius of the path of electrons?

Equation:

r = mV/Bq

B = .7 tesla
q = 1.6 x 10^-19 C

My problem here is that I don't know how to find the velocity of the electron for this equation. The supposed answer to the problem is 7.4 cm = r, but I'm just not getting that.
 
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  • #2
With an energy of 15 MeV, the electrons are clearly relativistic. The formula you're using is only valid in the non-relativistic regime.
 
  • #3
Do you know which equation I should be using then? This problem has been stumping me for days.

Thanks!
 
  • #4
That's something you should be able to derive on your own or at least find on your own in your textbook or notes.
 
  • #5
I was told to use the equation above by my professor. That's why I'm confused now.
 

Related to Electron Radius in a Bending Magnet

1. What is the electron radius in a bending magnet?

The electron radius in a bending magnet refers to the distance between the center of an electron's orbit and its outermost edge as it travels through a magnetic field.

2. How is the electron radius calculated?

The electron radius can be calculated using the formula r = mv/eB, where r is the radius, m is the mass of the electron, v is its velocity, e is its charge, and B is the strength of the magnetic field.

3. What is the significance of the electron radius in a bending magnet?

The electron radius is important in understanding the behavior of electrons in a magnetic field and is a key component in the design and operation of particle accelerators and other devices that use magnetic fields to manipulate charged particles.

4. How does the electron radius affect the trajectory of an electron in a bending magnet?

The electron radius determines the curvature of the electron's path as it travels through a magnetic field. A larger electron radius will result in a wider curvature, while a smaller electron radius will result in a tighter curvature.

5. Can the electron radius be changed?

Yes, the electron radius can be changed by altering the strength of the magnetic field or by changing the mass or velocity of the electron. It can also be affected by the presence of other charged particles in the vicinity.

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