Question Detail

Given: Electric field E = 1.2 x 105 N/C, charge q = 1.6 x 10-19 C, mass m = 9.1 x 10-31 kg, distance d = 20 mm = 0.02 m. The force on the electron is F = qE. Acceleration a = F/m = qE/m. a = (1.6 x 10-19 C * 1.2 x 105 N/C) / (9.1 x 10-31 kg) a = (1.92 x 10-14) / (9.1 x 10-31) ≈ 2.1099 x 1016 m/s². Since the electron starts from rest, we use the kinematic equation: d = (1/2)at². t = sqrt((2d)/a) = sqrt((2 * 0.02 m) / (2.1099 x 1016 m/s²)) t = sqrt(0.04 / (2.1099 x 1016)) = sqrt(0.018968 x 10-16) t = sqrt(1.8968 x 10-18) ≈ 1.377 x 10-9 s. None of the options exactly matches this value. However, if the electric field intensity was 1.2 x 103 N/C instead of 1.2 x 105 N/C (a factor of 100 difference), then: a' = (1.6 x 10-19 * 1.2 x 103) / (9.1 x 10-31) ≈ 2.1099 x 1014 m/s². t' = sqrt((2 * 0.02) / (2.1099 x 1014)) ≈ 1.377 x 10-8 s. Assuming a typo in the electric field magnitude, option C (1.38 x 10-8 s) is the closest calculated value.