FinalExam_Phys9HD_2009

# FinalExam_Phys9HD_2009 - FINAL EXAMINATION Physics 9HD Fall...

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1 FINAL EXAMINATION Physics 9HD Fall 2009 December 10, 2009 NAME_______________________________________________________________________ You are permitted to bring and use three 8 /1/2” x 11” sheets of paper with formulas, and your calculator. 8 QUESTIONS . MAXIMUM SCORE IS 150 POINTS. SHOW ALL OF YOUR WORK. ______________________________________________________________________________ 1. (30 points) You are going to calculate the properties of an ultrarelativistic proton, with mass m, as it passes first through an accelerating voltage, followed by a velocity selector. Assume that the initial velocity of the proton is zero. See the diagram of the arrangement in the lab frame below. (a) (5 points) The proton will gain energy from the accelerating voltage V along x ) . Find its velocity after it passes through the electric field caused by the accelerating voltage. (b) (5 points) Next, the proton passes through velocity selector, which is a region of crossed uniform electric and magnetic fields. The fields are both perpendicular to the particle’s velocity and to each other, i.e., z B B y E E x v v ) r ) r ) r = = = , , (see diagram). Derive an expression for the magnitude of the velocity v, in terms of the magnitudes of the electric and magnetic fields, E and B, if the proton’s velocity v is unchanged as it goes through this region, i.e., the proton successfully goes through the entrance slit to the velocity selector and leaves through the exit slit, with both slits along the x-axis, as shown. (c) (2 points) What is the work done by the magnetic field on the proton? (d) (10 points) Now consider the velocity selector from the rest frame of the proton. Since the proton went through the slits in the lab frame, the slits must go around the proton in the proton’s rest frame. Therefore, there must be no force acting on the proton in its rest frame. Show this by using the Lorentz transformation equations

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