Savchenko Solutions

Solutions of Savchenko Physics Textbook

Aliaksandr Melnichenka
October 2023

    <h3 id="back-link"><a href="/#2.3">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $2.3.39.$ One research institute decided to use an expression for the potential energy of point charges in the form $U' = \frac{kqQ}{r} - \frac{kqQ}{R}$, where $R$ is a constant distance set once and for all. Will using $U'$ instead of $U = \frac{kqQ}{r}$ affect the results of particle motion calculations?
    </p>

    <h3>Solution</h3>
    <p>
        $$

u = \frac{kqQ}{r}
$$

$$u' = \frac{kqQ}{r} - \frac{kqQ}{R}$$

$$R = \text{const}$$

$$(u_x)' = p$$

$$(u')' = - \frac{kqQ}{r^2} \, dr$$

$$(u')' = - \frac{kqQ}{r^2} \, dr$$

$$(\text{const})' = 0 \Rightarrow (R)' = 0$$

$$(u')' = (u')'!$$

$$u = u'!$$

$$\text{No, it won't!}$$

    <h4>Answer</h4>
    <p>
        No.
    </p>
    
    <p style="text-align: right; font-style: italic; font-size: 14;">   
      Almaskhan Arsen<br>
    </p>


<footer class="row container">
  <br>
    <p>
        <small> © <strong>Savchenko Solutions</strong>, 2023-2024 <br></small>
    </p>
    <p>
        <small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
    </p>
</footer>