10smidterm - Electromagnetic Theory II Midterm Examination...

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Electromagnetic Theory II Midterm Examination 3 March 2010 Instructions: There are 4 questions. Single part questions are worth 20 points, and 2 part questions are 15 points per part. Explain your reasoning in each case. Use SI units through- out. Points will be deducted for gaps in logic, for errors in calculation, and incorrect units. A sheet of useful formulas is provided at the end of the exam booklet. 1. A particle of charge q is moving in static uniform electric and magnetic fields that are perpendicular to each other. You may assume E = E ˆ y and B = B ˆ z , with 0 < E < cB . a) (15 points) Find all possible initial velocities v 0 such that the particle experiences no acceleration throughout its subsequent motion. b) (15 points) Find the magnitude of the magnetic field B 0 in an inertial frame in which the electric field E 0 = 0. (Hint: It is sufficient to consider invariants.) 1
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2. (20 points) A particle of charge q and mass m has an initial velocity with magnitude v = c/ 2, half the speed of light, and with direction perpendicular to a static uniform magnetic field B = B ˆ z , which is assumed to fill all of space. Show that the trajectory of the particle is circular and find the time it takes to complete one orbit.
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