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 4.21 m long and must accelerate protons from rest to a speed of 1.06 x 107 m/s. Ignore any relativistic effects and determine the magnitude of the average electric field that could accelerate these protons.

Answer 1

sqrt(2 a X) = V

Solve the above equation for the required acceleration, a, and then use

a = F/m = eE/m

to solve for the electric field E;

e and m are the proton charge and mass.