/*! 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} Q19E Suppose a force between two part... [FREE SOLUTION] | 91影视

91影视

Find study content
Learning Materials

Discover learning materials by subject, university or textbook.

Explanations

Textbooks
All Subjects

Anthropology

Archaeology

Architecture

Art and Design

Bengali

Biology

Business Studies

Greek

Chemistry

Chinese

Combined Science

Computer Science

Economics

Engineering

English

English Literature

Environmental Science

French

Geography

German

History

Hospitality and Tourism

Human Geography

Italian

Japanese

Law

Macroeconomics

Marketing

Math

Media Studies

Medicine

Microeconomics

Music

Nursing

Nutrition and Food Science

Physics

Polish

Politics

Psychology

Religious Studies

Sociology

Spanish

Sports Sciences

Translation

All Subjects

Biology

Business Studies

Chemistry

Combined Science

Computer Science

Economics

English

Environmental Science

Geography

History

Math

Physics

Psychology

Sociology
Features
Features

Discover all of these amazing features with a free account.

Flashcards

91影视 AI

Notes

Study Plans

Study Sets
What鈥檚 new?

Flashcards
Study your flashcards with three learning modes.

Study Sets
All of your learning materials stored in one place.

Notes
Create and edit notes or documents.

Study Plans
Organise your studies and prepare for exams.
91影视
Discover

All the hacks around your studies and career - in one place.

Find a degree

Magazine
Featured

Magazine
Trusted advice for anyone who wants to ace their studies & career.

The largest student job board with the most exciting opportunities.

Verified student deals from top brands.

Discover our mobile app to take your studies anywhere.

Learning Materials

Features

Discover

Chapter 12: Q19E (page 556)

Suppose a force between two particles decreases distance according to $F = k / r^{b}$ . What is the limit on b if the energy required to separate the particlesInfinitely far is not to be infinite?

Short Answer

Expert verified

The limit on b is $b > 1$ .

Step by step solution

01

Given data

A force between two particles decreases with distance, according to $F = k / r^{b}$ .

02

Concept of Potential energy

The force $F_{x}$ is the negative of the derivative of the potential energy U such that,

$F_{x} = - \frac{d U}{d x}$

Therefore, the differential form of the potential energy can be written as,

$d U = - F_{x} d x$

03

Calculation of the potential energy

Integrate the above equation on both sides, andgetthe expression for the total potential energy as:

$U (x) = - 鈭� F_{x} d x$

For force,the formula can be written as:

$F = \frac{k}{r^{b}}$

The energy of this force would be given as,

$U = - 鈭� F d r$

Substitute $F = \frac{k}{r^{b}}$ in the above equation as:

$\begin{array}{rcl} U & = & 鈭� \frac{k}{r^{b}} d r \\ U & = & - 鈭� k r^{- b} d r \\ U & = & - \frac{k r^{- b + 1}}{- b + 1} \end{array}$

When b is not 1 , we need $- b + 1 < 0$ to make sure the energy is not infinite at infinite separation, which is $b > 1$ . Thus, the limit on is $b > 1$

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!

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

In the following exercises, two protons are smashed together in an attempt to convert kinetic energy into mass and new particles. Indicate whether the proposed reaction is possible. If not, indicate which rules are violated. Consider only those for charge, angular momentum, and baryon number If the reaction is possible, calculate the minimum kinetic energy required of the colliding protons.

$p + p 鈫� 危^{+} + p + K^{0}$

Although not truly fundamental, the residual strong force shared by nucleons can also be represented by a feynmandiagram, with pion filling the role of mediating boson.The accompanying diagram represents a force between a neutron and a proton mediated by a $蟺^{0}$ boson.Suggest a diagram in which they exchange a $蟺^{-}$ particle.

In non-relavistic quantum mechanics, governed by the Schrodinger equation, the probability of finding a particle does not change with time.

(a)

Prove it, Begin with the time derivative of the total probability

$\frac{d}{d t} 鈭� 唯^{*} (x, t) 唯^{'} (x, t) d x = 鈭� (唯 (x, t) \frac{鈭�}{鈭� t} 唯^{*} (x, t) + 唯^{*} (x, t) \frac{鈭�}{鈭� t} 唯 (x, t)) d x$

Then use the Schrodinger equation to eliminate the partial time derivatives, integrate by parts, and show that the result is zero. Assume that the particle is well localised, so that $蠄鈥塧苍诲鈥� \frac{鈭� 蠄}{鈭� x}$ are 0 when evaluated at . $卤鈭�$

(b) Does this procedure lead to the same conclusion if Wave function obeyKlein-Gordon rather than Shrodinger equation? Why and why not?

Why would it be argued that the range of the strong force should be infinite, and why it isn鈥檛?

Sketch the Feynman diagram if the proposed decay is possible.

$螖^{+} 鈫� 危^{+} + 蟺^{0} + 纬$

See all solutions

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Electricity and Magnetism

Read Explanation

Astrophysics

Read Explanation

Translational Dynamics

Read Explanation

Engineering Physics

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.