Relativity

Problem 1

In this picture (from "Elementary Particles" , Harvard project  what about Giacomelli ?), you can see an electron spiralling in a hydrogen bubble chamber (link to Dora? or short explanation?). The size of the picture is 67% of the real size.

The incoming electron track starts from the bottom left. The bubble chamber is subject to a magnetic field B = 1.2 T perpendicular to the plane of the drawing. 

The electron is thus forced to move in a circular path of radius R=p/qB by the Lorentz force. As you can see, the radius gets smaller as the accelerating (going in a circle) electron emits radiation and loses energy.  (Link to who? accelerated charges emit radiation  )

EXERCISE:

1. Print the picture, draw a circle that fits the first few centimeters of the track and measure its radius. 

• Do not forget the scale! (the actual trajectory has a bigger radius). You can do it "by hand" (drawing several circles), but there is a geometrical procedure which you can see here (Link to Dora)

• You have to assume that you are measuring the real trajectory which, if that is true, must be in the plane of  the picture, but it could be otherwise! (Link to Alison.)
• Check your results against ours here.

3. Calculate the initial momentum of the electron.
4. Calculate the electron speed using p = mv. Does the result seem strange to you? If you know any other way of doing it, do it! If not, go to the next question.
5. You will find the question, with a hint,  here.

NOTE: In schools, we derive the equation p = qBR using non - relativistic mechanics, but it is also valid in special relativity (provided you do not substitute p for mv). Isn' t it  curious?

 Back to Startpage