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 4.00m long and must accelerate protons from rest to a speed of 1.0 x 107 m/s. Find:

a. average electric field that could accelerate these protons.

b. potential difference would be required to produce that average electric field. c. work done by electric field.

c. work done by the potential difference.

d. increase in proton kinetic energy.

e. gamma.

f. Do protons accelerate from high to low potential, or from low to high potential?

g. Is relativity required to get more precise answers?

h. Why do c, d, and e have the same values?

Answer 1

distance d=4.00 m initial speed v₀= 0 m/s   

     

(f) protons always accelerates from positive terminal to negative terminal i.e. higher potential to lower potential.

(g) yes relativity is required because proton travel at a speed comparable to speed of light. so its mass and energy will get modified according to special theory of relativity.

(h) answers of part c,d,e, are same due to work energy theorem i.e. change in energy=work done.