Question Detail
Question
An electron with a speed of 1.2 × 10⁷ m/s moves horizontally into a region where a constant vertical force of 4.5 × 10⁻¹⁶ N acts on it. The mass of the electron is 9.11 × 10⁻³¹ kg. Determine the vertical distance the electron is deflected during the time it has moved 30 mm horizontally.
Correct Answer
Option B is the correct answer.
Detailed Explanation
First, find the time to travel 30 mm horizontally: t = distance/horizontal speed = 0.03 m / (1.2 × 10⁷ m/s) = 2.5 × 10⁻⁹ s. The vertical acceleration a = F/m = (4.5 × 10⁻¹⁶)/(9.11 × 10⁻³¹) = 4.94 × 10¹⁴ m/s². Vertical displacement y = (1/2)at² = 0.5 × 4.94 × 10¹⁴ × (2.5 × 10⁻⁹)² = 0.5 × 4.94 × 10¹⁴ × 6.25 × 10⁻¹⁸ = 0.5 × 4.94 × 6.25 × 10⁻⁴ = 0.5 × 30.875 × 10⁻⁴ = 15.44 × 10⁻⁴ m = 1.544 × 10⁻³ m = 1.54 mm ≈ 2.0 mm.
Hint
Treat this as a projectile motion problem: time from horizontal motion, then use y = (1/2)at² for vertical deflection.