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Unformatted text preview: Electromagnetic Theory I Solution Set 1 Due: 29 August 2011 This and all future homework will be posted on the course webpage: http://www.phys.ufl.edu/ thorn/homepage/eminfo.html In the homework assignments, I will refer to problems in Jackson by prefixing the problem number with J. 1. a) Solve for the motion of a point particle with charge q and mass m in constant homoge- neous electric and magnetic fields that are perpendicular to each other. For definiteness take B = B z parallel to the z-axis and E = E y parallel to the y-axis. Take the initial condition that the particle is at rest at the origin of coordinates. You may assume that the speed of the particle remains much smaller than the speed of light throughout the motion. Solution: Use Lorentz force law and p m v to obtain: dv x dt = qB m v y , dv y dt =- qB m v x + qE m (1) d 2 v y dt 2 =- q 2 B 2 m 2 v y , d 2 v x dt 2 =- q 2 B 2 m 2 v x- E B (2) Clearly v x , v y harmonically oscillate at angular frequency = qB/m about the values E/B, 0 respectively. The solution for v x ( t ) , v y ( t ) with initial conditions v x (0) = v y (0) = 0 is v x ( t ) = dx dt = E B- E B cos t, v y ( t ) = dy dt = 1 dv x dt = E B sin t (3) Integrating these with respect to...
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This note was uploaded on 09/25/2011 for the course PHY 6346 taught by Professor Staff during the Spring '08 term at University of Florida.
- Spring '08