A uniform electric field exists in the region between two oppositely charged plane parallel plates. an electron is released from rest at the surface of the negatively charged plate and strikes the surface of the opposite plate, 3.20 cm distant from the first, in a time interval of 1.5 * 10^-8s. (a) find the magnitude of this electric field. (b) find the speed of the electron when it strikes the second plate.
To find the magnitude of the electric field, we can use the fact that the electron is accelerated by the electric field as it moves from one plate to the other.
(a) To find the magnitude of the electric field, we can use the equation of motion:
d = v0*t + (1/2)*a*t^2
where d is the distance traveled by the electron (3.20 cm), v0 is the initial velocity of the electron (which is zero since it starts from rest), t is the time interval (1.5 * 10^-8 s), and a is the acceleration of the electron.
Since the electron is accelerated by the electric field, the force on the electron can be calculated using the equation:
F = m*a
where F is the force on the electron, m is the mass of the electron, and a is the acceleration.
The force on the electron is also given by the equation:
F = |q| * E
where |q| is the magnitude of the charge of the electron, and E is the magnitude of the electric field.
Since we know the mass of the electron (9.11 * 10^-31 kg) and the charge of the electron (1.6 * 10^-19 C), we can solve for the acceleration of the electron:
a = F / m = |q| * E / m
Now we can substitute this expression for acceleration into the equation of motion:
d = (1/2) * (|q| * E / m) * t^2
Solving for the magnitude of the electric field (E):
E = (2 * d * m) / (|q| * t^2)
Substituting the given values (d = 3.20 cm = 0.0320 m, m = 9.11 * 10^-31 kg, |q| = 1.6 * 10^-19 C, and t = 1.5 * 10^-8 s), we can calculate E.
(b) To find the speed of the electron when it strikes the second plate, we can use the equations of motion:
v = v0 + a*t
where v is the final velocity of the electron, v0 is the initial velocity of the electron (which is zero), a is the acceleration of the electron (which we already calculated in part a), and t is the time interval.
Substituting the given values (t = 1.5 * 10^-8 s and a = calculated from part a), we can calculate v.