An electron accelerates from rest through a potential difference of 184 V. What is its final speed?
An electron that has a horizontal initial speed of 4.50 106 m/s enters a region that has an electric field of 120 V/m pointing vertically upward.
How long does the electron take to travel 24 cm in the horizontal direction
In this same time, what is the vertical displacement of the electron? Treat up as positive
(Voltage change)*charge = kinetic energy change.
Use that to get the K.E and then use that and the electron mass to get the final velocity.
For the second question,
(travel time, t) = 0.24 m/(horizontal velocity)
Vertical displacement = (1/2) a t^2
Get the acceleration a from
a = F/m = e*E/m
E is the Electric field, which is given. e is the electron charge.
To find the final speed of an electron accelerated through a potential difference, we can use the formula:
final speed = square root(2 * e * V / m)
where:
- e is the charge of an electron (1.6 * 10^-19 C)
- V is the potential difference across which the electron is accelerated (184 V)
- m is the mass of an electron (9.1 * 10^-31 kg)
By substituting the given values into the formula and performing the calculations, we can find the final speed of the electron:
final speed = square root(2 * (1.6 * 10^-19 C) * (184 V) / (9.1 * 10^-31 kg))
Solving this equation will give us the final speed in m/s.
To find the time it takes for an electron to travel a certain distance in the presence of an electric field, we can use the formula:
time = distance / initial horizontal speed
where:
- distance is the horizontal displacement of the electron (24 cm = 0.24 m)
- initial horizontal speed is the speed at which the electron enters the region (4.50 * 10^6 m/s)
By substituting the given values into the formula, we can calculate the time taken by the electron to travel the given distance.
To find the vertical displacement of the electron in the same time, we can use the formula:
vertical displacement = (1/2) * acceleration * time^2
where:
- acceleration is the acceleration due to the electric field (120 V/m)
- time is the time taken by the electron to travel the horizontal distance (calculated in the previous step)
By substituting the given values into the formula, we can calculate the vertical displacement of the electron. Since the acceleration is directed upwards, the displacement will be positive if the electron moves up.
Performing these calculations will provide the answers to the given questions.