CHAPTER 21
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Figure 21.63 on page 617 of your text shows the tracks of an electron (charge -e) and an antielectron (charge +e) created in a bubble chamber. When the particles made these tracks, they were under the influence of a magnetic field of 1.0 T in a direction perpendicular to and into the plane of the figure. What is the momentum of each particle? Assume that they are moving in the plane of the figure and that this figure is 1/10 of natural size. Which is the track of the electron and which is the track of the antielectron (positron)?
While you will need to get a ruler and measure the radii of the tracks in your book in a little while, we can begin without the text. A simplified sketch of the bubble chamber tracks is found below. (The sketch is not-to-scale and introduces a third color to aid in describing the process.)
The yellow track is that of a photon. This high-energy photon has more than 1 MeV of energy and is in the very short x-ray or gamma ray region. The point at which the yellow track ends and the green and red tracks begin marks where the electron and positron are created. A positron is a particle with the same mass as an electron, but with a +e charge.
The magnetic force is the centripetal force that causes the particles to move in circular orbits. The decrease in the radii of the orbits occurs because the particles' energies are decreasing (the real-life world of the bubble chamber). The vector nature of the force equations will enable us to determine which track was made by the electron and which was from the positron.
With this vector equation in hand, we examine the top track alone.
The direction of the cross-product is found by using the right-hand rule. (Take your right hand and put your fingers in the direction of the velocity vector, keeping your thumb out - away from your other fingers. Since we want to cross this into the magnetic field that is pointing directly into the page, you should have the palm of your right hand facing the page. Now, rotate your hand so that your fingers are in the direction of the magnetic field. Your thumb should be in the direction of the cross-product as shown in the sketch.)
Next, we move to the magnitude of the electron's momentum. Since we want to use these equations again for the other track, we hold-off on putting the numbers into the equation.
It is time to pull out a ruler and your textbook. Measure the outer most diameter of the top track from the creation point. Since the figure is 1/10 of natural size, we need to multiply the diameter by ten to obtain the actual diameter of the electron's path. Substituting the values into the equation above (be certain to divide the diameter by two to get the radius), we find the electron's momentum is as follows.
Moving to the bottom path, we use much of the work done above to determine the particle's momentum. A sketch of the bottom path is found below.
The direction of the cross-product is determined via the right-hand rule.
Upon measuring the diameter of the positron's path, we immediately plug into the momentum equation from above to find the positron's momentum.
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