Figure 29.21 shows a charged particle traveling in a non-uniform magnetic field forming a magnetic bottle.
(a) Explain why the positively charged particle in the figure must be moving clockwise. The particle travels along a helix whose radius decreases and whose pitch decreases as the particle moves into a stronger magnetic field. If the particle is moving to the right along the x axis, its velocity in this direction will be reduced to zero and it will be reflected from the right-hand side of the bottle, acting as a “magnetic mirror.” The particle ends up bouncing back and forth between the ends of the bottle.
(b) Explain qualitatively why the axial velocity is reduced to zero as the particle moves into the region of strong magnetic field at the end of the bottle.
(c) Explain why the tangential velocity increases as the particle approaches the end of the bottle.
(d) Explain why the orbiting particle has a magnetic dipole moment.
(e) Sketch the magnetic moment and use the result of Problem 17 to explain again how the non-uniform magnetic field exerts a force on the orbiting particle along the x axis.