A 10.0-μF capacitor has plates with vacuum between them....

A $10.0-\mu \mathrm{F}$ capacitor has plates with vacuum between them. Each plate carries a charge of magnitude $1000 \mu \mathrm{C}$. A particle with charge $-3.00 \mu \mathrm{C}$ and mass $2.00 \times 10^{-16} \mathrm{kg}$ is fired from the positive plate toward the negative plate with an initial speed of $2.00 \times 10^{6} \mathrm{m} / \mathrm{s} .$ Does it reach the negative plate? If so, find its impact speed. If not, what fraction of the way across the capacitor does it travel?

Key Concepts

Parallel Plate Capacitor

A parallel plate capacitor consists of two conductive plates separated by an insulating material (or vacuum) and stores electric charge and energy. Its behavior is characterized by its capacitance, which determines how much charge it can store for a given voltage difference. This concept is fundamental in understanding how electric fields and potentials are established in devices that store electrical energy.

Electric Field in a Capacitor

The electric field between the plates of a capacitor is generally uniform and can be determined by the potential difference between the plates divided by the separation distance. This electric field exerts forces on charged particles placed within it and is central to analyzing their motion in problems involving parallel plate capacitors.

Force on a Charged Particle in an Electric Field

A charged particle in an electric field experiences a force given by the product of its charge and the electric field. This force, determined by F = qE, is responsible for accelerating the particle, and its direction depends on the sign of the charge relative to the direction of the field. This concept is key when evaluating the dynamics of particles moving between capacitor plates.

Energy Conservation in Electric Fields

Energy conservation in the context of charged particle motion involves the interplay between kinetic energy and electric potential energy. As a charged particle moves in an electric field, potential energy is converted into kinetic energy (or vice versa). Analyzing this energy conversion allows one to determine whether the particle has sufficient energy to overcome a potential barrier and reach a particular point, such as moving from one capacitor plate to the other.

Please give Ace some feedback