Physics 325 Spring 2011 Problem Session 3

Physics 325 Spring 2011 Problem Session 3 - we can choose...

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Physics 325 Spring 2011 Discussion 3 February 7, 2011 Let us revisit the example of a charged particle (mass m , charge q ) in a uniform constant magnetic ﬁeld ~ B = B ˆ z . This time, we use the cylindrical coordinates ( r,φ,z ) . (a) Write down the equations of motion in cylindrical components ( ˙ v r , ˙ v φ , and ˙ v z ). Start from ~v = v r ˆ r + v φ ˆ φ + v z ˆ z and take time derivative of both sides. Remember that both ˆ r and ˆ φ have non-zero time derivative. (b) Suppose the initial velocity is given, with v z = 0 at t = 0 . Without loss of generality,
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Unformatted text preview: we can choose the origin of coordinates such that v r = 0 at t = 0 . Let v =-u at t = 0 . Even with this restriction, we still have a freedom to choose the value of r at t = 0 . What should we choose for r at t = 0 such that we have v r = 0 initially? (c) Solve for v r ( t ) and v ( t ) with the initial conditions from part (b). Hint: You may need to use a result from differential equations about rst order equations....
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This note was uploaded on 10/06/2011 for the course PHYS 325 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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