Question

A tiny hole is made in the center of the negatively and positively charged plates of a capacitor, allowing a beam of electrons to pass through and emerge from the far side. If $40.0 \mathrm{V}$ are applied across the capacitor plates and the electrons enter through the hole in the negatively charged plate with a speed of $2.50 \times 10^{6} \mathrm{m} / \mathrm{s},$ what is the speed of the electrons as they emerge from the hole in the positive plate?

Name: Problem 67, Chapter 17: Physics
Uploaded: 2020-06-23T22:09:46-08:00
Duration: 2 min 40 s
Channel: Mayukh Banik

   A tiny hole is made in the center of the negatively and positively charged plates of a capacitor, allowing a beam of electrons to pass through and emerge from the far side. If $40.0 \mathrm{V}$ are applied across the capacitor plates and the electrons enter through the hole in the negatively charged plate with a speed of $2.50 \times 10^{6} \mathrm{m} / \mathrm{s},$ what is the speed of the electrons as they emerge from the hole in the positive plate?

Physics

Robert Coleman… 5th Edition

Chapter 17, Problem 67

Instant Answer

Solved by Expert Mayukh Banik

06/23/2020

Step 1

First, we need to find the initial kinetic energy of the electrons when they enter the hole in the negatively charged plate. We can use the formula for kinetic energy: KE = (1/2)mv^2, where m is the mass of an electron and v is its velocity. Show more…

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A tiny hole is made in the center of the negatively and positively charged plates of a capacitor, allowing a beam of electrons to pass through and emerge from the far side. If $40.0 \mathrm{V}$ are applied across the capacitor plates and the electrons enter through the hole in the negatively charged plate with a speed of $2.50 \times 10^{6} \mathrm{m} / \mathrm{s},$ what is the speed of the electrons as they emerge from the hole in the positive plate?

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Key Concepts

Conservation of Energy

This principle states that the total energy in a closed system remains constant. In the context of charged particles in an electric field, the work done by the electric field (through the potential difference) is fully converted into kinetic energy, which allows one to calculate the particle’s final speed after acceleration.

Electric Potential Difference and Work

A voltage difference applied across electrodes results in an electric field that does work on charged particles. The work done on a charge is given by the product of the charge and the voltage, which represents the energy transferred from the field to the particle.

Kinetic Energy of a Particle

The kinetic energy of a moving particle is given by the equation ½mv². When a charged particle gains energy from an electric field, this gained energy adds to its initial kinetic energy, thereby increasing its speed based on the relationship between energy and velocity.

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