Problems are listed in approximate order of difficulty. A single dot (•) indicates straigh...

Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.

•• Thomson directed his cathode rays at a metal body and measured the total charge Q that it acquired and its rise in temperature ΔT. From ΔT and the body’s known thermal capacity, he could find the heat given to the body. Show that this heat should be

where m, v, and e are the electron’s mass, speed (nonrelativistic), and charge. Combine this with the result of Problem 1 to give expressions for v and m/e in terms of measured quantities.

Problem 1

•• Suppose that the electrons in Thomson’s experiment enter a uniform magnetic field B, which is in the z direction (with axes defined as in Fig. 1) and has total width l. Show that they are deflected through an angle θ ≈ eBl/(mv) (provided that θ is small). Assume that the electrons are nonrelativistic.

FIGURE 1