Problem Breakdown:

You have a uniform electric field between two plates, and electrons are accelerated through the field. We are tasked with calculating the acceleration of the electron when subjected to this electric field. The electric field strength is given as $E = 2.40 \times 10^4 \, \text{N/C}$.

Key Concepts:

1. Force on an Electron in an Electric Field: The force $F$ on a charged particle (like an electron) in an electric field is given by Coulomb's law: $F = qE$ where:

   • $q$ is the charge of the electron ($q = -1.6 \times 10^{-19} \, \text{C}$),
   • $E$ is the electric field strength.

2. Acceleration of the Electron: Using Newton's second law, the acceleration $a$ of the electron is related to the force by: $a = \frac{F}{m}$ where:

   • $m$ is the mass of the electron ($m = 9.11 \times 10^{-31} \, \text{kg}$).

Step-by-Step Solution:

1. Calculate the Force on the Electron: $F = qE = (-1.6 \times 10^{-19} \, \text{C}) \times (2.40 \times 10^4 \, \text{N/C})$ $F = -3.84 \times 10^{-15} \, \text{N}$ The negative sign indicates that the force is directed toward the positive plate (since the electron is negatively charged and the electric field points from the positive to the negative plate).

2. Calculate the Acceleration: Using Newton's second law: $a = \frac{F}{m} = \frac{-3.84 \times 10^{-15} \, \text{N}}{9.11 \times 10^{-31} \, \text{kg}}$ $a = -4.22 \times 10^{15} \, \text{m/s}^2$ The negative sign indicates the direction of acceleration, but for magnitude, we simply consider: $a = 4.22 \times 10^{15} \, \text{m/s}^2$

Thus, the acceleration of the electron is approximately $4.22 \times 10^{15} \, \text{m/s}^2$.

Explanation of Electron's Motion Through the Hole:

• Once the electron passes through the hole in the positive plate, it will not be pulled back toward the plate because:
  • The electron is moving at a high speed as it exits the hole.
  • The electric field between the plates can no longer affect it in the same way, because it has passed the region where the field is uniform.
  • The absence of the field means no force is acting on it anymore, so it continues its motion in a straight line according to Newton's first law (inertia).
  • Therefore, unless acted upon by another force (e.g., magnetic fields or collisions), the electron will continue moving away from the positive plate.

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Would you like more details or any clarification? Here are some related questions you can explore:

1. How does the direction of the electric field affect the motion of the electron?
2. What would happen if the electron had a higher initial velocity when it was released near the negative plate?
3. How does the mass of the electron affect its acceleration in the electric field?
4. What other forces (besides the electric force) could potentially act on an electron in this setup?
5. How would the acceleration change if the electric field strength were increased or decreased?

Tip: Always keep track of the direction of forces and accelerations—since they can sometimes cause confusion, especially when dealing with charged particles!