# A linear accelerator designed to produce a beam of 800-MeV protons has 2000 accelerating tubes. What average

## Question:

A linear accelerator designed to produce a beam of 800-MeV protons has 2000 accelerating tubes. What average voltage must be applied between tubes (such as in the gaps in Figure 33.9) to achieve the desired energy?

Strategy

The energy given to the proton in each gap between tubes is PEelec = qV where q is the proton's charge and Vis the potential difference (voltage) across the gap. Since q = qe = 1.6 x 10-19 C and 1 eV =(1 V)(1.6 x 10-19 C), the proton gains 1 eV in energy for each volt across the gap that it passes through. The AC voltage applied to the tubes is timed so that it adds to the energy in each gap. The effective voltage is the sum of the gap voltages and equals 800 MV to give each proton an energy of 800 MeV.

Data from figure 33.9

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