A simple and common technique for accelerating electrons is...

A simple and common technique for accelerating electrons is shown in Figure $7.46,$ where there is a uniform electric field between two plates. Electrons are released, usually from a hot filament, near the negative plate, and there is a small hole in the positive plate that allows the electrons to continue moving. (a) Calculate the acceleration of the electron if the field strength is $2.50 \times 10^{4} \mathrm{N} / \mathrm{C} .$ (b) Explain why the electron will not be pulled back to the positive plate once it moves through the hole.

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Key Concepts

Uniform Electric Field

A uniform electric field is defined as a region where the strength and direction of the electric field remain constant. It is an essential concept for understanding how forces act on charged particles over a given area, leading to predictable motion and acceleration when subjected to this field.

Electric Force on a Charge

The force experienced by a charge in an electric field is given by the equation F = qE, where q is the charge and E is the electric field strength. This fundamental relationship is crucial for determining the dynamics of charged particles when they are exposed to an electric field.

Newton's Second Law of Motion

Newton's second law, expressed as F = ma, links the net force acting on an object to its acceleration and mass. In the context of charged particles, it provides a method to calculate acceleration from the electric force, forming the basis for analyzing motion under the influence of electric fields.

Motion of Charged Particles

The motion of charged particles in electric fields encompasses the study of their trajectories, acceleration, and velocities as influenced by electrostatic forces. This concept is central to disciplines such as electromagnetism and particle dynamics, describing how particles continue moving under specific initial conditions and field configurations.

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