The 3.20-kilometre-long Stanford Linear Collider at SLAC (Stanford Linear Accelerator Laboratory) produces a beam of 50.0 giga electron volt electrons. If there are 15000 accelerating tubes, what average voltage must be across the gaps between them to achieve this energy?
We’re told in this statement that the electrons in the beam produced by the collider have an energy of 50.0 giga electron volts. We’re also told there are 15000 accelerating tubes, each of which contributes to the acceleration of the electrons in the beam. We want to know the average voltage across each of the tubes, what we’ll call 𝑉 sub avg.
𝑉 sub avg will be equal to the total energy supplied to the electrons divided by the number of tubes. Each electron in the beam is supplied with 50.0 giga volts or 50.0 times 10 to the ninth volts of energy, and there are 15000 tubes. When we calculate this fraction, we find a result of 3.33 times 10 to the sixth volts or 3.33 mega volts. That’s the average voltage across each of the accelerating tubes.