An electron with a speed of 1.9 × 107 m/s moves horizontally into a region where a constant vertical force of 5.4 × 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 46 mm horizontally.
To determine the vertical distance the electron is deflected, we need to find the time it takes for the electron to move horizontally 46 mm, and then use that time and the given force to calculate the vertical displacement.
First, let's convert the horizontal distance from millimeters to meters:
46 mm = 46 × 10^-3 m
Next, we can use the speed of the electron to find the time it takes to move the horizontal distance. The formula to calculate time is distance divided by speed:
time = distance / speed
Plugging in the values:
time = (46 × 10^-3 m) / (1.9 × 10^7 m/s)
Evaluating the above expression:
time = 2.42 × 10^-9 seconds
Now that we have the time, we can calculate the vertical displacement using the formula:
displacement = (force × time^2) / (2 × mass)
Plugging in the values:
displacement = (5.4 × 10^-16 N × (2.42 × 10^-9 s)^2) / (2 × 9.11 × 10^-31 kg)
Evaluating the expression:
displacement = 1.36 × 10^-6 meters
Therefore, the vertical distance the electron is deflected during the time it has moved 46 mm horizontally is approximately 1.36 × 10^-6 meters.