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Unformatted text preview: Physics 105B Problem Set 9 June 3, 2008 Jeff Schonert: schonert (at) physics.ucsb.edu Taylor 15.80 Refer to the equation of motion listed in problem 15.79: F = m a + ( F v ) v /c 2 Since the magnetic force is perpendicular to both v and B , this means that F v = 0 We also know that magnetic forces cannot change the speed of a particle; they can only change its direction. Therefore, v is a constant, meaning that is a constant as well. Plugging these into the above force equation, we get that m v = e ( v B ) This is the same as the non-relativistic equation except now m has been replaced by m . So the physics of the particle is basically the same, with this minor mass modification. Therefore, if v is initially orthogonal to B , then it will stay orthogonal. This perpendicular force will result in circular motion with radius r = mv eB = p eB Taylor 15.87 Let the pion initially be traveling along the x-axis, so that the two photons are traveling in the xy-plane. Initial 4-momentum is denoted p and the two final 4-momenta are p 1 and p 2 . Conservation of momentum requires that p = p 1 + p 2 . Because the pion has no momentum in the y-direction, its 4-momentum is ( E /c, p , , 0) , meaning that the y-momenta of the two photons must add up to zero in order to have conservation of momentum. Therefore,conservation of momentum....
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