An electron enters the region of a uniform electric field, with v1=3*10^6 m/s and E=200N/C. The horizontal length of the plates is 0.100m
1. Fine the acceleration of the electron while in the field.
2. If the electron enters the field at a time t=0, find the time at which it leaves the field.
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To find the acceleration of the electron while in the electric field, we can use the equation F = ma, where F is the force experienced by the electron, m is the mass of the electron, and a is the acceleration.
1. Calculating the force on the electron:
The force experienced by an electron in an electric field is given by the equation F = qE, where q is the charge of the electron and E is the electric field strength.
In this case, the charge of an electron is -1.6 x 10^-19 C, and the electric field strength is given as 200 N/C. Thus, the force on the electron is:
F = qE
F = (-1.6 x 10^-19 C)(200 N/C)
F = -3.2 x 10^-17 N
Note: The negative sign indicates that the force is acting in the opposite direction of the electric field.
2. Finding the acceleration:
Since the force experienced by the electron is given, we can use F = ma to find the acceleration. Rearranging the equation, we get:
a = F/m
The mass of an electron is approximately 9.11 x 10^-31 kg. Substituting the known values, we have:
a = (-3.2 x 10^-17 N) / (9.11 x 10^-31 kg)
a ≈ -3.51 x 10^13 m/s^2
The negative sign indicates that the acceleration is in the opposite direction of the electric field.
Now, let's move on to the second part of the question.
To find the time at which the electron leaves the electric field, we need to consider the distance traversed by the electron and its initial velocity.
3. Calculating the distance traveled by the electron:
The distance traveled by the electron can be determined using the equation d = v1 * t, where d is the distance, v1 is the initial velocity, and t is the time.
The horizontal length of the plates, which represents the distance traveled by the electron, is given as 0.100 m.
4. Determining the time at which the electron leaves the field:
To find the time at which the electron leaves the field, we can rearrange the distance equation:
t = d / v1
Substituting the values, we get:
t = (0.100 m) / (3 x 10^6 m/s)
t ≈ 3.33 x 10^-8 s
Therefore, the electron leaves the field after approximately 3.33 x 10^-8 seconds.