Question

Problem 1:Let’s discuss some particle physics. In 1897, physicist J.J. Thomson conducted a seminalexperiment with a cathode ray tube. In the experiment, a beam of an unknown particle of chargeqandmassmis shot through the tube onto a fluorescent screen, at some speedvand in thex-direction. Uponimpact the beam leaves a bright spot on the screen. Sincevis very fast, effects of gravity are negligible andthe beam forms essentially a straight line normal to the screen.

(a) A uniform nonzero electric field−→E=Eˆzis then turned on by parallel plates of edge lengthLinsidethe tube. As the beam passes between the plates, it experiences deflection due to the electric force andemerges out of the plates by some displacement ∆z. What is ∆z?

(b) To eliminate this deflection, an external uniform magnetic field of magnitudeBis turned on as well.What should be the direction and magnitudeBof this field such that ∆z= 0?

(c) By using the results in parts (a) and (b), we can find the ratio|q|/mof the unknown particle. Whatis|q|/m?

(d) When Thomson conducted his experiment, it was still believed that the atom was the smallest unit ofmatter, making the hydrogen cation the lightest charged particle known back then. When Thomsonconducted his experiment, however, the|q|/mvalue of his mysterious beam was about 1000(!) timeslarger than the|q|/mfor the hydrogen cation. Based on this result, what conclusion can you drawabout the hypothesis that the hydrogen cation is the lightest charged particle?

This experiment was the first discovery of the existence of a subatomic particle. Just for fun, do you knowwhat Thomson’s mysterious particle was? (The chargeqof this particle was measured in a later experimentby Robert A. Millikan in 1909.)

Answer 1