(a) ¿Cuál es la velocidad final de un electrón acelerado...

Name: Problem 94, Chapter 7: Física Universitaria Volumen 2
Uploaded: 2020-07-09T23:46:00-08:00
Duration: 2 min 56 s
Channel: Luis Rios
Description: (a) ¿Cuál es la velocidad final de un electrón acelerado desde el reposo a través de un voltaje de 25,0 MV por un terminal de Van de Graff cargado negativamente? (b) ¿Qué no es razonable en este resultado? (c) ¿Qué suposiciones son responsables?

(a) ¿Cuál es la velocidad final de un electrón acelerado desde el reposo a través de un voltaje de 25,0 MV por un terminal de Van de Graff cargado negativamente? (b) ¿Qué no es razonable en este resultado? (c) ¿Qué suposiciones son responsables?

Key Concepts

Energy Conversion in Electric Fields

This concept involves converting electrical potential energy into kinetic energy when a charged particle is accelerated through a voltage difference. It is based on the work done by the electric field on the particle, which is equal to the product of the charge and the voltage change. This principle is fundamental when calculating the motion and final kinetic energy of charged particles in devices like accelerators.

Relativistic Kinetic Energy

When a charged particle, such as an electron, is accelerated to very high speeds, its kinetic energy is no longer accurately described by classical (non-relativistic) formulas. Instead, relativistic kinetic energy, which takes into account the effects of special relativity, must be used. This concept ensures that the calculations adhere to the principle that no object can exceed the speed of light.

Non-Relativistic vs. Relativistic Approaches

In many problems involving particle acceleration, classical equations like (1/2)mv² can be used for low speeds. However, when the particle’s speed approaches a significant fraction of the speed of light, these formulas fail to predict accurate results. The necessity for relativistic formulas arises from the fact that classical mechanics does not respect the universal speed limit imposed by the speed of light, highlighting the importance of choosing the correct theoretical framework based on the particle's energy.

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