The Tolma-Stewart experiment in 1916 demonstrated that the free charges in a metal have n...

The Tolma-Stewart experiment in 1916 demonstrated that the free charges in a metal have negative charge and provided a quantitative measurement of their charge – to – 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 to the right. Initially the free charges in the metal lag behind the rod’s motion, thus setting up an electric field in the rod. In the steady state this field exerts a force on the free that makes them accelerate along with the rod. (a) Apply to the free charges to obtain an expression for |q|/m interms of the magnitudes of the induced electric field and the acceleration . (b) If all the free charges in the metal rod have the same acceleration the electric field 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 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 × 10−19 C, mass 9.11 × 10−31 kg), what magnitude of acceleration is required to produce a potential difference of 1.0 mV between the 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.

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