The figure below shows an electron entering a uniform electric field perpendicularly betweenthe middle of two plates with a velocity of 5.0 × 107 m s−1. Two flat parallel plates, each oflength 12.0 cm, are separated by a distance of 1.5 cm.The potential difference between the plates is 210 V.(a) Calculate the magnitude of the electric field strength between the plates.(b) Determine the magnitude and direction of the acceleration of the electron.(c) Calculate the time for the electron to travel a horizontal distance equal to the length of theplates.(d) Use your answers in (c) to determine whether the electron will hit one of the plates oremerge from between the plates.
Question
The figure below shows an electron entering a uniform electric field perpendicularly betweenthe middle of two plates with a velocity of 5.0 × 107 m s−1. Two flat parallel plates, each oflength 12.0 cm, are separated by a distance of 1.5 cm.The potential difference between the plates is 210 V.(a) Calculate the magnitude of the electric field strength between the plates.(b) Determine the magnitude and direction of the acceleration of the electron.(c) Calculate the time for the electron to travel a horizontal distance equal to the length of theplates.(d) Use your answers in (c) to determine whether the electron will hit one of the plates oremerge from between the plates.
Solution
(a) The electric field strength (E) between the plates can be calculated using the formula E = V/d, where V is the potential difference and d is the distance between the plates.
E = 210 V / 0.015 m = 14,000 N/C
(b) The force (F) on the electron due to the electric field can be calculated using the formula F = qE, where q is the charge of the electron. The charge of an electron is -1.6 x 10^-19 C.
F = (-1.6 x 10^-19 C) * (14,000 N/C) = -2.24 x 10^-15 N
The acceleration (a) of the electron can be calculated using the formula F = ma, where m is the mass of the electron. The mass of an electron is 9.11 x 10^-31 kg.
a = F/m = -2.24 x 10^-15 N / 9.11 x 10^-31 kg = 2.46 x 10^15 m/s^2
The negative sign indicates that the acceleration is in the opposite direction to the electric field, i.e., downwards.
(c) The time (t) for the electron to travel a horizontal distance equal to the length of the plates can be calculated using the formula t = d/v, where d is the distance and v is the velocity.
t = 0.12 m / 5.0 x 10^7 m/s = 2.4 x 10^-9 s
(d) The vertical distance (d) the electron will travel due to its acceleration can be calculated using the formula d = 0.5at^2, where a is the acceleration and t is the time.
d = 0.5 * 2.46 x 10^15 m/s^2 * (2.4 x 10^-9 s)^2 = 7.07 x 10^-3 m
Since this distance is greater than the separation between the plates (1.5 cm or 0.015 m), the electron will hit one of the plates before it can emerge from between them.
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