An electron and a proton having mass m_e and m_p respectively, initially at rest, move through the same distance ' s ' in a uniform electric field ' E '. If the time taken by them to cover that distance is t_e and t_p respectively, then t_e / t_p is equal to:

Step-by-step solution

The force experienced by a particle of charge q in a uniform electric field E is given by F = qE . Using Newton's second law, the acceleration a of the particle is a = F m = qE m . For a particle starting from rest, the distance s covered in time t is given by the kinematic equation s = 1 2 at^2 . Substituting the expression for acceleration, we have s = 1 2 ( qE m ) t^2 , which implies t = 2sm qE . Since the electron and proton have the same magnitude of charge e , the same distance s , and are in the same electri