set1 - Department of Physics The Ohio State University Prof...

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Department of Physics Prof. R. Bundschuh The Ohio State University First Problem Set for Physics 664 (Theoretical Mechanics) Spring quarter 2004 Important dates: Apr 27 9:30am-10:18am & May 11 9:30am-10:18am midterm exams, May 31 no class, Jun 9 9:30am-11:18am final exam Due date: Thursday, Apr 8 1. Charged particle in electromagnetic fields 14 points We consider a particle of mass m and charge q in a homogeneous electric field ~ E and a homogeneous magnetic field ~ B . Thus, the particle is subject to the Lorentz force ~ F = q ~ E + q~v × ~ B where ~v is the (instantaneous) velocity of the particle and we assume that the absolute value of this velocity is much smaller than the speed of light at all times. Without loss of generality we assume that the magnetic field is parallel to the z axis, i.e., ~ B = B~e z , and that the electric field is in the y - z -plane, i.e., E x = 0. a) Let us first assume that ~ E = 0 and that the initial velocity ~v 0 of the particle is within the x - y -plane. Show that the trajectory of the particle is a circle with radius r = m | ~v 0 | /qB

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