A 4.15-volt battery is connected across a parallel-plate...

A 4.15-volt battery is connected across a parallel-plate capacitor. Illuminating the plates with ultraviolet light causes electrons to be emitted from the plates with a speed of $1.76 \times 10^{6} \mathrm{~m} / \mathrm{s} .$ (a) Suppose electrons are emitted near the center of the negative plate and travel perpendicular to that plate toward the opposite plate. Find the speed of the electrons when they reach the positive plate. $(b)$ Suppose instead that electrons are emitted perpendicular to the positive plate. Find their speed when they reach the negative plate.

Key Concepts

Photoelectric Effect

The photoelectric effect describes the emission of electrons from a material when it is exposed to electromagnetic radiation, such as ultraviolet light. In problems like this, it is important to recognize that the emitted electrons initially have a given kinetic energy and that subsequent acceleration in an electric field alters their speed. This concept links the quantum behavior of electron emission with classical electromagnetism.

Conservation of Energy in Electric Fields

This concept states that when a charged particle moves in an electric field, its kinetic energy changes by an amount equal to the work done by the field. In the context of a capacitor, a particle gains or loses kinetic energy equivalent to the product of its charge and the potential difference it traverses. This principle is fundamental in analyzing how an electron's speed changes as it moves between the plates.

Electric Potential Difference and Work

The potential difference between two points establishes how much work is done on a charge moving between those points. For an electron moving in a capacitor, the potential energy change (given by the electron charge multiplied by the voltage difference) is converted into kinetic energy; this explains the acceleration or deceleration experienced by the electron depending on its initial direction relative to the electric field.

Uniform Electric Field in a Parallel-Plate Capacitor

In a parallel-plate capacitor, the electric field is uniform between the plates. This uniformity simplifies the calculation of work done on a charge since the force is constant over the distance between the plates. Understanding this concept is crucial for correctly applying energy conservation to determine the change in kinetic energy of the electron.

Transcript

Please give Ace some feedback