Physics 110B: Homework 2 - Problems and Solutions, Assignments of Psychology

Download Physics 110B: Homework 2 - Problems and Solutions and more Assignments Psychology in PDF only on Docsity! Phys 110B: Problems for HW 2 C. Gwinn, W09 January 11, 2009 1 HW2 Problem 1 Monopoles Note: Dirac originally worked out this problem. The existence and role of monopoles remains controversial among theorists, and a goal for experimentalists. A simple model for a magnetic monopole is a very thin, half-infinite solenoid. Suppose that the solenoid extends from −∞ to 0 along the z-axis. The monopole lies at the origin: at the end of the solenoid. Except inside the solenoid (which we choose to ignore), the magnetic field is: ~B(~r) = µ0 4π g r2 r̂, (1) where g is the magnetic charge of the monopole. a) Suppose that an electron (with charge −e) approaches the monopole from far away. at high speed v, with impact parameter b. Specifically, far away the electron is at position (x, y, z) = (−∞, 0, b) and it velocity is (vx, vy, vz) = (+v0, 0, 0). Estimate the effect of the interaction by estimating the change in momentum ∆~p, as given by the impulse ~F∆t. For your estimate, take ~F as constant, equal to the force at the closest approach b (if the electron were undeflected), and ∆t as the time for the electron to travel twice a distance b. (This crude approximation is good in the limit of large b and/or large v0; it’s also good in these limits, with the correct force law, for Rutherford scattering.) What is the final speed and direction of the electron? b) Find the initial angular momentum of the electron about the origin ~L0, and its final angular momentum ~L1. Find the change in angular momentum ∆~L. Show that this change is independent of b. 1