An electron with a horizontal speed of 4.0 * 10^6 m/s an no vertical component of velocity passes through two horizontal plates. The magnitude of the electric field between the plates is 150 n/c. The
To find the distance traveled by the electron between the plates, we need to use the equations of motion and the known values of the electron's horizontal speed, the magnitude of the electric field, and the absence of a vertical component of velocity.
We can start by using Newton's second law, which states that the net force acting on an object is equal to the object's mass times its acceleration. In this case, the net force is the force due to the electric field, and the acceleration is the horizontal component of the electron's acceleration.
The force due to the electric field can be calculated using the equation F = qE, where F is the force, q is the charge, and E is the electric field. For an electron, the charge is -e (the elementary charge).
Since the electron is traveling in a horizontal direction, there is no vertical component of velocity. Therefore, the net force acting on the electron is the force due to the electric field.
Now, we can find the acceleration of the electron using the equation F = ma, where F is the force, m is the mass of the electron, and a is the acceleration.
Plugging in the known values, we have:
qE = ma
(-e)(150) = m * a
Since the mass of an electron is approximately 9.11 * 10^-31 kg and the elementary charge is -1.6 * 10^-19 C, we can substitute these values into the equation:
(-1.6 * 10^-19)(150) = (9.11 * 10^-31) * a
Simplifying the equation gives us:
-2.4 * 10^-17 = (9.11 * 10^-31) * a
To find the acceleration, we divide both sides of the equation by (9.11 * 10^-31):
a = -2.4 * 10^-17 / (9.11 * 10^-31)
Calculating this yields:
a = -2.63 * 10^13 m/s^2
Now that we have the acceleration, we can find the time taken by the electron to travel between the plates using the equation:
v = u + at
where:
v = final velocity (which is 4.0 * 10^6 m/s),
u = initial velocity (which is 0 m/s),
a = acceleration (which is -2.63 * 10^13 m/s^2), and
t = time taken.
Plugging in these values, the equation becomes:
4.0 * 10^6 = 0 + (-2.63 * 10^13) * t
Simplifying the equation gives:
4.0 * 10^6 = -2.63 * 10^13 * t
To isolate t, we divide both sides of the equation by (-2.63 * 10^13):
t = (4.0 * 10^6) / (-2.63 * 10^13)
Calculating this yields:
t = -1.52 * 10^-7 s
Since time cannot be negative, we take the absolute value of t:
t = 1.52 * 10^-7 s
The distance traveled by the electron between the plates can now be determined using the equation:
d = ut + 0.5at^2
where:
d = distance traveled,
u = initial velocity (which is 0 m/s),
t = time taken (which is 1.52 * 10^-7 s), and
a = acceleration (which is -2.63 * 10^13 m/s^2).
Plugging in these values, the equation becomes:
d = 0 + 0.5 * (-2.63 * 10^13) * (1.52 * 10^-7)^2
Simplifying the equation gives:
d = -1.57 * 10^-6 m
Since distance cannot be negative, we take the absolute value of d:
d = 1.57 * 10^-6 m
Therefore, the distance traveled by the electron between the plates is approximately 1.57 * 10^-6 meters.