Question

Subscribe For this discussion, respond to the following.. An electron falls through a distance d in a uniform electric field of magnitude E. Thereafter, the direction of the field is reversed (keeping its magnitude the same) and now a proton falls through the same distance. Compare, using quantitative reasoning, the time of fall in each case. Contrast this situation with that of objects falling freely under gravity

Answer 1

Acceleration of a charge in uniform electric field is, a = qE/m Using Newton's equation of motion, d = ut + 1/2 at^2 d = 1/2 at^2 (Since, the charge is starting from rest u = 0) Therefore, time of fall is, t = squareroot 2d/a t = squareroot 2dm/qE For both electron and proton, the magnitude of charge is equal to e. However, their masses are different. Therefore, t_p/t_e = squareroot m_p/m_e t_p/t_e = squareroot 1.67 times 10^-27/9.11 times 10^-31 t_p/t_e = 42.82 Heavier particle (proton) will take more time to fall through the distance d. In case of free-fall, time of fall doesn't depend on the mass of the falling body. Acceleration due to gravity is ignored here because acceleration of proton and electron is very large compared to g.