Question Detail
Question
An electron is situated in a uniform electric field of intensity 1.2 x 103 N/C. Calculate the time it takes to travel 20mm from rest if the charge is 1.6x10-19 C and the mass is 9.1x10-31 kg.
Correct Answer
Option C is the correct answer.
Detailed Explanation
First, calculate the force (F) on the electron:F = qE = (1.6 × 10-19 C) × (1.2 × 103 N/C) = 1.92 × 10-16 N.Next, calculate the acceleration (a) of the electron using Newton's second law (F=ma):a = F/m = (1.92 × 10-16 N) / (9.1 × 10-31 kg) ≈ 2.1099 × 1014 m/s2.Now, use the kinematic equation for displacement (d) from rest: d = v0t + (1/2)at2. Since v0 = 0:d = (1/2)at2.Given d = 20 mm = 0.02 m.t2 = 2d / a = (2 × 0.02 m) / (2.1099 × 1014 m/s2) = 0.04 / (2.1099 × 1014) ≈ 1.8968 × 10-16 s2.t = √(1.8968 × 10-16 s2) ≈ 1.377 × 10-8 s.Rounding to two significant figures, t ≈ 1.38 × 10-8 s.(Note: The original question likely had a typo in the electric field intensity, as 1.2 x 105 N/C would yield a different result. Assuming 1.2 x 103 N/C to match option C).
Hint
First, find the force on the electron using F = qE. Then, calculate its acceleration using F = ma. Finally, use a kinematic equation to find the time it takes to travel the given distance, starting from rest: d = (1/2)at2.