Particle Tracks and Relativity

    The Spiral 

In this picture [1,2], you can see an electron spiralling in a hydrogen bubble chamber. 

The size of the picture is 67% of the real size[2].

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 (because it is going in a circle) electron emits radiation and loses energy. The electron also loses energy due to ionization[1,2]. 

    Now we will try to find the velocity of the electron at the beginning of the track

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" trying to draw the circle that fits best.  There is a geometrical procedure which you can see. Click here to see a PowerPoint Presentation 

• In this exercise we can assume that the trajectory is in the plane of  the picture. But in most cases, it is not so, and you need two or more different views of the event. If you want to know more on this, click here

• Here you can check your results against ours.