520 points. A schematic (top view) for a mass spectrometer is shown in the figure. The first stage is the box S (lower left chamber in the figure) which produces identical negative ions. Each ion has a mass m and charge -q. The ions then enter the second stage, which is a pair of plates at potential V and V. This potential difference accelerates each ion, essentially from rest to a speed v. One such ion is shown between the two plates. Each ion is moving at a speed v when it then enters the third stage, which is a chamber enclosing a uniform magnetic field. Once in the chamber, this field causes the ion to move in a 90° semicircle as shown until it deposits on the side of the chamber at a distance x from where it entered.
a) If the speed of the negative ion increases between the plates, is V or V' at higher potential?
b) What is the direction of the magnetic field in the chamber? Modify the figure to indicate the direction of this field throughout the chamber.
c) Determine an expression for the mass of the ion in terms of B, q, x, V, V' (not v), and other required constant(s).
