Question

86. Two uniformly charged plates carrying opposite charges are separated by a distance of 20 mm. The magnitude of the charge density on each plate is 3 X 10-8 C/m. An electron is launched with a speed of 2.1 X 106 m/s halfway between the two plates. (a) How far does the electron travel before it hits one of the plates? (b) What speed does the electron attain before it hits a plate?.

Answer 1

Sigma = 3 times 10^-8 c/m^2 electric field in between the plates E = sigma/epsilon_0 = 3 times 10^-8/8.85 times 10^-12 N/c Force on electron F = eE as shown u_x = 2.1 times 10^6m/s a_x = 0, a_y F/M = u_y = 0 eE/m s_y = 10mm = 10 times 10 times 10^-3m s_y = u_y t + 1/2 ay t^2 10 times 10^-3 = 0 + 1/2 times 1.6 times 10^-19 times 3 times 10^-8 t^2/8.85 times 10^-12 times 9.1 times 10^-31 t^2 = 1610.7 times 10^-46/4.8 times 10^-27 = 335.5625 times 10^-19 t = 57.93 times 10^-10 sec s_x = 2.1 times 10^6 times 57.93 times 10^-10m = 1.22 times 10^-2m v_y = v_y + a_y t = 0 times 1.6 10^-19 times 3 times 10^-8 times 57.93 times 10^-10/8.85 times 10^-12 times 9.1 times 10^-31 = 3.453 times 10^6 m/s \r\n speed v = squareroot v_x^2 + v^2_y = squareroot (2.1 times 10^6)