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.

•• The formulas for the deflection of an electron in an electric or magnetic field (Problems 1 and 2) are quite similar. Explain in words why both formulas have factors of v in the denominator and why the magnetic deflection has just one power of v where the electric has two.

Problem 1 and 2

1.•• In Thomson’s experiment electrons travel with velocity v in the x direction. They enter a uniform electric field E, which points in the y direction and has total width l (Fig. 1). Find the time for an electron to cross the field and the y component of its velocity when it leaves the field. Hence show that its velocity is deflected through an angle θ ≈ eEl/(mv2) (provided that θ is small). Assume that the electrons are nonrelativistic, as was the case for Thomson.

2.•• 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