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Modern Physics
Found in: Page 556
Modern Physics

Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

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Short Answer

Suppose a force between two particles decreases distance according to F=k/rb . What is the limit on b if the energy required to separate the particles Infinitely far is not to be infinite?

The limit on b is b > 1 .

See the step by step solution

Step by Step Solution

Step 1: Given data

A force between two particles decreases with distance, according to F=k/rb .

Step 2: Concept of Potential energy

The force Fx is the negative of the derivative of the potential energy U such that,


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


Step 3: Calculation of the potential energy

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


For force,the formula can be written as:


The energy of this force would be given as,


Substitute F=krb in the above equation as:


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

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