ch37-p055 - 55. Using the classical orbital radius formula...

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55. Using the classical orbital radius formula 0 /| | rm vq B = , the period is 00 2/2/ | | . Tr v m q B π = = In the relativistic limit, we must use 0 || pm v rr qB qB γ === which yields 0 22 TT B == = (b) The period T is not independent of v . (c) We interpret the given 10.0 MeV to be the kinetic energy of the electron. In order to make use of the mc 2 value for the electron given in Table 37-3 (511 keV = 0.511 MeV) we write the classical kinetic energy formula as Km v m c v c mc classical F H G I K J = 1 2 1 2 1 2 2 2 c h c h β . If K classical = 10.0 MeV, then = 2 2100 0511 6 256 2 K mc classical MeV MeV . . ., bg which, of course, is impossible (see the Ultimate Speed subsection of §37-2). If we use this value anyway, then the classical orbital radius formula yields () ( ) ( ) 31 8 3 19 9.11 10 kg 6.256 2.998 10 m/s 4.85 10 m. 1.6 10 C 2.20T mv m c r qB eB ×× = × × (d) Before using the relativistically correct orbital radius formula, we must compute
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ch37-p055 - 55. Using the classical orbital radius formula...

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