A proton is fired with a speed of 3.00 X 10^6 m/s directly towards a large and positively charged plane of surface charge density +9.25 X 10^-7 C/m^2 . If the proton starts 1m from the plane, the minimum distance between the proton and the plane is closest to.. ?

Question

A proton is fired with a speed of 3.00 X 10^6 m/s directly towards a large and positively charged plane of surface charge density +9.25 X 10^-7 C/m^2 . If the proton starts 1m from the plane, the minimum distance between the proton and the plane is closest to.. ?
A) 0cm   B) 10cm   C) 45cm  D) 55cm  E) 90cm

I know the answer is B, but not quite sure why :S

Any help would be appreciated, thank you.

drwls · Answer

Use the surface charge density to compute the E field perpendicular to the plate. The field will be independent of distance from the plate, if the plate is large compared to the distance from the plate.

E = (charge density)/(epsilon-zero)

Minimum distance occurs when the work done by the proton against the field the field equals the initial kinetic energy.

Be sure to subtract the distabnce travelled from 1 meter to get the distance from the wall at turnaround.