The Tolman-Stewart experiment in 1916 demonstrated that the free charges in a metal have negative charge and provided a quantitative measurement of their charge-w-mass ratio, |q|/m. The experiment consisted of abruptly stopping a rapidly rotating spool of wire and measuring the potential difference that this produced between the ends of the wire. In a simplified model of this experiment, consider a metal rod of length L that is given a uniform acceleration a to the right. Initially the free charges in the metal lag behind the rod's motion, thus setting up an electric field E in the rod. In the steady state this field exerts a force on the free charges that makes them accelerate along with the rod. (a) Apply ΣF = ma to the free charges to obtain an expression for |q|/m in terms of the magnitudes of the induced electric field E and the acceleration a. (b) If all the free charges in the metal rod have the same acceleration, the electric field E is the same at all points in the rod. Use this fact to rewrite the expression for |q|/m in terms of the potential Vbc between the ends of the rod (Fig.).
(c) If the free charges have negative charge, which end of the rod, b or c, is at higher potential?
(d) If the rod is 0.50 m long and the free charges are electrons (charge q = -1.60 X l0-19 C, mass 9.11 X l0-31 kg), what magnitude of acceleration is required to produce a potential difference of 1.0 mV between me ends of the rod?
(e) Discuss why the actual experiment used a rotating spool of thin wire rather than a moving bar as in our simplified analysis.The Tolman-Stewart experiment in 1916 demonstrated that the free charges in a metal have negative charge and provided a quantitative measurement of their charge-w-mass ratio, |q|/m. The experiment consisted of abruptly stopping a rapidly rotating spool of wire and measuring the potential difference that this produced between the ends of the wire. In a simplified model of this experiment, consider a metal rod of length L that is given a uniform acceleration a to the right. Initially the free charges in the metal lag behind the rod's motion, thus setting up an electric field E in the rod. In the steady state this field exerts a force on the free charges that makes them accelerate along with the rod. (a) Apply ΣF = ma to the free charges to obtain an expression for |q|/m in terms of the magnitudes of the induced electric field E and the acceleration a.