1) In the diagram below a uniform magnetic field of magnitude 0.09 T is directed vertically as shown. The two arrows that are superimposed on the field lines represent an electron (lower) and proton (upper). Each particle has 100 ev of kinetic energy and the velocity vectors shown each make 39° angles with the field direction.
a) The "eyeball" represents an observer. Redraw the diagram to show both the field direction (in or out) and the perpendicular components of each velocity vector as would be seen by an observer looking up (like the eyeball). Sketch the magnetic force vector that acts on each particle. Explain1 briefly how you know.
b) The particles execute helical trajectories. For each particle describe the circulation associated with the helix as either clockwise or counterclockwise and explain how you know.
c) Over a 10 second interval how many helical cycles does each particle complete. Determine the radius and pitch of each helix.
d) Which particle has a greater displacement along the field direction over the 10 s interval? Explain/show how you know.
2) As was demonstrated in class, two wires in proximity to each other and carrying current that flows in the same direction will exert attractive forces on each other. The two wires below each carry 5.2 amps of current and 0.6 m long sections of each wire are in proximity to each other. Each wire exerts a 0.4 N force on the other at the separation distance shown. In this context each wire can be viewed as interacting with the magnetic field produced by the other wire at its position.
a) Determine the magnitude of the magnetic field vectors produced by wire 2 along the length of wire 1 (i.e at wire 1's location). Assume the field is uniform over this length.
b) The force that acts on wire 1 can be described by the vector equation: F1 = IL x B2 . Using this equation2, the right hand rule and the fact that the wires attract, determine the direction of the magnetic field vectors produced by wire 2 at wire 1's location. You must explain your answer.
c) The wires would still attract if wire 1 were now to the right of wire 2. In which direction would the magnetic field vectors produced by wire 2 now point? Explain how you know using the same reasoning as in part b.
3) The space between two charged metal plates is filled with a uniform electric field as shown below. A beam of ions enters the device as shown. The plates are part of a velocity selector used to allow only those particles, from the ion beam, that enter the device with a specific velocity to pass through undeflected. A uniform magnetic field is also needed.
a) Assume that the ions are positively charged. In which direction does the magnetic field need to be directed for the device to work? Would your answer be different if the ions were negatively charged? Explain your reasoning.
b) Draw a free-body diagram (showing the electric and magnetic forces only) for a positively charged ion that passes undeflected through the device. Repeat for a negatively charged ion. Clearly label each force.
c) Uniform fields E and B, chosen so that ions with a velocity Vs pass through the selector undeflected, are maintained in the regiom between the plates. Sketch the trajectory and free body diagram for a positively charged ion that enters the device with a speed that exceeds Vs ( = Vs ). The lengths of the force arrows in the free body diagram should reflect the relative magnitudes of the forces. Repeat for a negatively charged ion with the same speed. Briefly explain your reasoning in each case.
4) The device diagrammed below is a mass spectrometer. It has three main components: a chamber where a uniform magnetic field of magnitude 0.0014 T directed into the page is maintained, a velocity selector as in question 3 and an accelerator which uses an electric field to accelerate ions of atomic oxygen essentially from rest. There are two movable collectors attached to the chamber and the magnetic field is used to steer ions into the collectors. The beam of ions consists of several isotopes of oxygen: 16O (mass=15.995 amu ) 17O (mass=16.999 amu ) and 18O (mass=17.999 amu) . 1 amu=1.66 x 10-27 kg. All of the ions are missing one electron (singly ionized) and they enter the velocity selector with a range of velocities that overlaps the selector's "undeflected " velocity.
If the electric and magnetic fields in the velocity selector have magnitudes 235.0 N/C and 0.045 T respectively,
a) Determine the speed at which the 16O ions enter the chamber. Repeat for the ) 17O ions. Does the mass of the ion affect the speed at which it enters the chamber?
b) Determine the position of the two collectors, relative to the selector opening into the chamber, so that 16O and 17O are collected. Repeat for 17O and 18O.
c) Will the device as shown work for negatively charged ions with the same masses? If not, what would have to be different? Explain your reasoning.
