/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 70 What is the acceleration of an e... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 15: Problem 70

What is the acceleration of an electron that is placed in a uniform electric field of \(6500 \mathrm{~N} / \mathrm{C}\) pointing in the \(+y\) -direction?

Short Answer

Expert verified
The acceleration is \(-1.14 \times 10^{15} \, \text{m/s}^2\) in the \(-y\) direction.

Step by step solution

01

Identify Given Values

We are given an electric field of strength \( E = 6500 \, \text{N/C} \) and we know the charge \( q \) and mass \( m \) of an electron are \( q = -1.6 \times 10^{-19} \, \text{C} \) and \( m = 9.11 \times 10^{-31} \, \text{kg} \), respectively.
02

Use the Electric Force Equation

The force \( F \) on a charge \( q \) in an electric field \( E \) is calculated as \( F = qE \). Substitute the values: \[ F = (-1.6 \times 10^{-19} \, \text{C})(6500 \, \text{N/C}) = -1.04 \times 10^{-15} \, \text{N} \], indicating a force in the \(-y\) direction.
03

Use Newton's Second Law to Find Acceleration

According to Newton's second law, \( F = ma \), where \( a \) is the acceleration. Rearrange this to solve for acceleration: \( a = \frac{F}{m} \). Substitute the force and mass values: \[ a = \frac{-1.04 \times 10^{-15} \, \text{N}}{9.11 \times 10^{-31} \, \text{kg}} \approx -1.14 \times 10^{15} \, \text{m/s}^2 \].

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electron Properties
Electrons are fundamental particles with unique characteristics that make them key to understanding electric phenomena. They have a negative electric charge denoted as \( q = -1.6 \times 10^{-19} \, \text{C} \). This negative charge implies that they move opposite to the direction of the electric field.
Besides their charge, electrons have a small mass compared to other subatomic particles. The mass of an electron is approximately \( m = 9.11 \times 10^{-31} \, \text{kg} \). Despite their lightweight nature, electrons significantly influence both atomic behavior and macroscopic electric fields. The combination of charge and mass influences how they will accelerate when exposed to electric fields, which is crucial in everything from simple circuits to advanced technologies like particle accelerators.
Newton's Second Law
Newton's Second Law of Motion is fundamental when dealing with forces and acceleration. This law is stated as \( F = ma \), meaning the force acting on an object is equal to its mass multiplied by its acceleration.
When applying this law to an electron in an electric field, the force \( F \) experienced by the electron can be calculated using the equation \( F = qE \), where \( E \) is the electric field strength. Knowing the charge of the electron and the electric field allows us to find the force applied to it.
  • Rearranging Newton's Second Law gives us \( a = \frac{F}{m} \), which determines the acceleration \( a \) of the electron when the force \( F \) and mass \( m \) are known.
  • This relationship shows why small particles, like electrons, can achieve significant accelerations in electric fields despite their tiny masses.
Understanding this principle helps explain the rapid movement of electrons in electric circuits and semiconductor devices.
Electric Force
The concept of electric force is critical to understanding how charged particles interact within an electric field. The electric force \( F \) acting on a charged particle is a result of the particle being in an electric field, calculated using the formula \( F = qE \). Here, \( q \) is the charge of the particle and \( E \) is the electric field strength.
For an electron, the negative charge alters the direction of the force compared to positively charged particles. In our exercise, this results in a force directed opposite to the electric field.
  • Understanding electric force allows us to calculate the resulting acceleration, using the force in Newton's Second Law, \( a = \frac{F}{m} \).
  • This force is responsible for moving particles, enabling technologies such as cathode ray tubes, accelerators in physics research, and various electronic devices.
Mastery of the concept is essential for predicting and manipulating the behavior of charges in electric fields.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

BIO = Forces in a DNA molecule. In a chemical reaction, the two ends of a \(2.45-\mu \mathrm{m}\) -long DNA molecule acquire charges of \(+e\) and \(-e,\) res pectively. What is the force between the two ends of the molecule?

An electric dipole on the \(x\) -axis consists of a charge \(-Q\) at \(x=-d\) and a charge \(+Q\) at \(x=+d\). (a) Find a general expression (in terms of \(Q\) and \(d\) ) for the electric field at points on the \(x\) -axis with \(x>d\). (b) Show that for \(x \gg d\) the magnitude of the field you computed in part (a) is a pproximately equal to \(E=4 k Q d / x^{3}\) and therefore approximates an inverse-cube distance law.

A proton moving at \(3.8 \times 10^{5} \mathrm{~m} / \mathrm{s}\) to the right enters a region where a uniform electric field of magnitude \(56 \mathrm{kN} / \mathrm{C}\) points to the left. (a) How far will the proton travel before it stops moving? (b) What will happen to the proton after it stops moving? (c) Graph the proton's position versus time, velocity versus time, and acceleration versus time after it enters the field.

Which one of the following is true regarding a proton and an electron in identical electric fields? (a) The force on the electron is larger. (b) The force on the proton is larger. (c) The acceleration of the electron is larger. (d) The acceleration of the proton is larger.

Assume that the hydrogen atom consists of an electron in a circular orbit around a proton, with an orbital radius of \(5.29 \times 10^{-11} \mathrm{~m}\). (a) What is the electric field acting on the electron? (b) Use your answer in part (a) to find the force acting on the electron.
See all solutions

Recommended explanations on Physics Textbooks

Fundamentals of Physics

Read Explanation

Thermodynamics

Read Explanation

Quantum Physics

Read Explanation

Electricity

Read Explanation

Measurements

Read Explanation

Magnetism

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.