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Problems are listed in approximate order of difficulty. A single dot (•) indicates straigh...

Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.

•• Protons are injected into a linear accelerator so that they have K = 250 keV as they coast through the first drift tube. The frequency of the AC voltage applied to the tubes is 50 MHz and the peak potential difference across each gap is 200 kV. Consider a proton that passes from the first to the second tube properly synchronized at the peak potential drop, (a) How long must the second tube be if the proton is to arrive at the next gap in proper synchronization with the accelerating voltage? (b) How long must the tenth tube be?

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