Question

A proton and an electron are released from rest at the same time from the midpoint between two charged parallel plates. The plates are charged with equal surface charge densities of opposite signs. Ignore the interaction between the electron and the proton and consider only the interaction of each charge with the electric field of the plates. After being released, the proton will accelerate toward the negative plate, and the electron will accelerate toward the positive plate. (a) Which charge will reach the plate first? the proton the electron They will both reach the plate at the same time. If tp and te are the times taken for the proton and electron to reach the plate, calculate the ratioP te (b) Which charge hits the plate moving the fastest? the proton the electron They both reach the plate at the same speed. If vp and ve are the speeds of the proton and electron as they hit the plate, calculate the ratioP

Answer 1

Let E is the uniform electric field in between the plates a_p = F_p/m_p = e E/m p a_e = e E/m e using S = ut + 1/2 at^2 for proton d/2 = 0 + 1 /2 a_p t^2_p rightdoublearrow t_p = squareroot dm_p/e E for electrons d/2 = 0 + 1/2 a_c t^2_c rightdoublearrow t_c squareroot dm_e/eE t_p/t_c = squareroot m_e/m_c rightdoublearrow t_p/t_c = squareroot 1836/1 = 42.85 electrons wil reach the plate first (b) using v^2 = u^2 + 2as v^2_p = 2 a_p d/2 = eE d/m_p v_p = squareroot eEd/m_p and v_e = squareroot eEd/m_e v_p/v_e = squareroot m_e/m_p = squareroot 1/1836 = 1/ 42.85 rightdoublearrow electron wil strike with large velocity