Chapter 22, Problem 27PCE

Helical Motion As a model of the physics of the aurora, consider a proton emitted by the Sun that encounters the magnetic field of the Earth while traveling at 4.3 × 10⁵ m/s. (a) The proton arrives at an angle of 33° from the direction of $\stackrel{\to }{B}$ (refer to Figure 22-19). What is the radius of the circular portion of its path if B = 3.5 × 10⁻⁵ T? (b) Calculate the time required for the proton to complete one circular orbit in the magnetic field. (c) How far parallel to the magnetic field does the proton travel during the time to complete a circular orbit? This is called the pitch of its helical motion.