Question

Some forms of cancer can be treated using proton therapy in which proton beams are accelerated to high energies, then directed to collide into a tumor, killing the malignant cells. Suppose a proton accelerator is 4.0 m long and must accelerate protons from rest to a speed of 1.0 × 107 m/s. Ignore any relativistic effects (Chapter 26) and determine the magnitude of the average electric field that could accelerate these protons.

Answer 1

F = q E = m a = m (Vf/t)
but t = distance/average velocity
and average velocity = Vf/2
so t = 2d/Vf
so
q E = m Vf (Vf/2d) = m Vf^2/2d

E = m Vf^2 /(2qd)