2. Focusing a beam of electrons In the Cornell Electron Storage Ring (CESR)', a beam of electrons circulates at speeds of roughly 0.9999995 times the speed of light c. The beam tends to spread out as it travels (due in part to the mutual repulsion of the electrons), so lenses in the form of quadrupole magnets are used to focus the beam. For a beam traveling in the +3 direction. the eld inside the magnet is where g is some positive constant (a) Show that the divergence of this field is zero, as it must be to satisfy Gauss's law for the magnetic field. (b) Find the magnetic force on an electron moving parallel to the axis with (r, y) coordinates (z, 0). (Take the velocity to be v = ck.) Does the force focus or defocus the beam? Is its magntiude proportional to r, so electrons farther away from the z-axis get deflected through a larger angle? (c) Find the magnetic force on an electron moving parallel to the axis with (r, y) coordinates (0, y). Does the force focus or defocus the beam