Chapter 23, Problem 23.80P

DATA A small, stationary sphere carries a net charge Q. You perform the following experiment to measure Q: From a large distance you fire a small particle with mass m = 4.00 × 10⁻⁴ kg and charge q = 5.00 × 10⁻⁸ C directly at the center of the sphere. The apparatus you are using measures the particle’s speed υ as a function of the distance x from the sphere. The sphere’s mass is much greater than the mass of the projectile particle, so you assume that the sphere remains at rest. All of the measured values of x are much larger than the radius of cither object, so you treat both objects as point particles. You plot your data on a graph of υ² versus (1 /x) (Fig. P23.80). The straight line υ² = 400m²/s² − [(15.75 m³/s²)/x] gives a good fit to the data points, (a) Explain why the graph is a straight line, (b) What is the initial speed υ₀ of the particle when it is very far from the sphere? (c) What is Q? (d) How close does the particle get to the sphere? Assume that this distance is much larger than the radii of the particle and sphere, so continue to treat them as point particles and to assume that the sphere remains at rest.

Figure P23.80