As we've seen in class, in a uniform magnetic field that is perpendicular to a particle's direction of motion, the particle will follow a circular path. Let's derive some additional quantities for this situation. You should also know from Physics I that an object undergoing circular motion experiences an acceleration (pointed inward): a = v2/R where R is the circle's radius. (a) Combine that acceleration with the magnetic force law, along with your knowledge of Newton's Second Law, to find an algebraic expression for the radius of the circular path that a charge moving in a uniform magnetic field will trace out. (b) Now recall from Physics I that the frequency of a circular motion (i.c., the number of times that the object completes a circle per second) is given by f = v/(2#R), the speed divided by the circle's circumference. If you want to make an electron complete a circle once per second, what strength magnetic field must you set it moving within? (c) One important application of this phenomenon is the mass spectrometer: you can determine a particle's mass via the curve it traces in a magnetic field. Suppose a subatomic particle follows a curved path in a magnetic field (which is pointed perpendicular to the particle's motion), as shown in the diagram. Is the particle positively or negatively charged? The particles speed is measure to be 3.2 x 106 m/s as it moves along a circular path of radius 47 mm in a 1.5 T magnetic field. If it is singly charged, so that lol = e, what is its mass? X