Solved: The Tolma-Stewart experiment in 1916 demonstrated

Chapter 25, Problem 85CP

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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-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 \(\vec{a}\) to the right. Initially the free charges in the metal lag behind the rod’s motion, thus setting up an electric field \(\vec{E}\) 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 \(\Sigma \vec{F}=m \vec{a}\) to the free charges to obtain an expression for \(|q| / m\) in terms of the magnitudes of the induced electric field \(\vec{E}\) and the acceleration \(\vec{a}\). (b) If all the free charges in the metal rod have the same acceleration, the electric field \(\vec{E}\) is the same at all points in the rod. Use this fact to rewrite the expression for \(|q| / m\) in terms of the potential \(V_{b c}\) between the ends of the rod (Fig. P25.85). (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 \(q=-1.60 \times 10^{-19}\) C, mass \(9.11 \times 10^{-31}\) 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.

Equation Transcription:

Text Transcription:

|q|/m

Vector a

Vector E

SigmaVector F=mvector a

|q|/m

Vector E

Vector a

Vector E

|q|/m

V_bc

q=-1.60x10^-19

9.11x10^-31