Added Luis's English solution of 7.1.3
en/7.1.3.md
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| + | <!DOCTYPE html> | ||
| + | <html lang="en"> | ||
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| + | <head> | ||
| + | <meta charset="utf-8"> | ||
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| + | <title>Savchenko Solutions</title> | ||
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| + | <script type="text/x-mathjax-config"> | ||
| + | MathJax.Hub.Config({ | ||
| + | extensions: ['tex2jax.js'], | ||
| + | jax: ['input/TeX', 'output/HTML-CSS'], | ||
| + | tex2jax: { | ||
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| + | }); | ||
| + | </script> | ||
| + | </head> | ||
| + | <body style=""> | ||
| + | <header style="text-align:center;"> | ||
| + | <h2>Solutions of Savchenko Physics Textbook</h2> | ||
| + | <p class="author"> | ||
| + | Aliaksandr Melnichenka <br/> | ||
| + | October 2023 | ||
| + | </p> | ||
| + | </header> | ||
| + | |||
| + | <h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3> | ||
| + | |||
| + | <h3> Statement </h3> | ||
| + | |||
| + | <p> | ||
| + | $7.1.3$ | ||
| + | A particle with a charge $q$ and a mass $m$ passes through a region of a uniform electric field of length $d$ in time $t$. The velocity $v$ of a particle entering the field is directed along the field. Determine the electric field intensity. | ||
| + | </p> | ||
| + | |||
| + | <h3>Solution</h3> | ||
| + | <p> | ||
| + | The motion of particle is accelerated by electric field, so | ||
| + | $$d = vt-\frac{at^2}{2} \;(1)$$ | ||
| + | Applying Newton Second Law | ||
| + | $$F = qE = ma$$ | ||
| + | then, | ||
| + | $$a = \frac{qE}{m} \;(2)$$ | ||
| + | Putting $(2)$ into $(1)$ | ||
| + | $$\boxed{E = 2m\frac{d-vt}{qt^2}}$$ | ||
| + | </p> | ||
| + | <p style="text-align: right; font-style: italic; font-size: 14;"> | ||
| + | BSc. Luis Daniel Fernández Quintana<br> | ||
| + | Physics Department (FCNE)<br> | ||
| + | Universidad de Oriente, Cuba<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> | ||
| + | </body> | ||
| + | |||
| + | </html> | ||
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| <!DOCTYPE html> | |||
| <html lang="en"> | |||
| <head> | |||
| <meta charset="utf-8"> | |||
| <meta name="viewport" content="width=device-width, initial-scale=1.0"> | |||
| <meta http-equiv="content-language" content="en"> | |||
| <meta name="keywords" content="solutions, savchenko, physics problems, olympiad physics, physics book"> | |||
| <meta name="description" content="A website with solutions to physics problems from Savchenko Textbook"> | |||
| <meta property="og:title" content="Savchenko Solutions"> | |||
| <meta property="og:image" content="img/logo.png"> | |||
| <meta property="og:description" content="A website with solutions to physics problems from Savchenko Textbook"> | |||
| <meta name="yandex-verification" content="6cfda41f74038368"> | |||
| <title>Savchenko Solutions</title> | |||
| <link rel="stylesheet" href="https://savchenko-physics.github.io/css/css-latex/style.css"> | |||
| <link rel="icon" href="https://savchenko-physics.github.io/img/logo.png" type="image/png"> | |||
| <script src="https://savchenko-physics.github.io/js/jquery-1.10.1.min.js"></script> | |||
| <script async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML"></script> | |||
| <script type="text/x-mathjax-config"> | |||
| MathJax.Hub.Config({ | |||
| extensions: ['tex2jax.js'], | |||
| jax: ['input/TeX', 'output/HTML-CSS'], | |||
| tex2jax: { | |||
| inlineMath: [['$', '$'], ['$', '$']], | |||
| processEscapes: true, | |||
| processClass: 'tex2jax', | |||
| ignoreClass: 'html' | |||
| }, | |||
| showProcessingMessages: false, | |||
| messageStyle: 'none' | |||
| }); | |||
| </script> | |||
| </head> | |||
| <body style=""> | |||
| <header style="text-align:center;"> | |||
| <h2>Solutions of Savchenko Physics Textbook</h2> | |||
| <p class="author"> | |||
| Aliaksandr Melnichenka <br/> | |||
| October 2023 | |||
| </p> | |||
| </header> | |||
| <h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3> | |||
| <h3> Statement </h3> | |||
| <p> | |||
| $7.1.3$ | |||
| A particle with a charge $q$ and a mass $m$ passes through a region of a uniform electric field of length $d$ in time $t$. The velocity $v$ of a particle entering the field is directed along the field. Determine the electric field intensity. | |||
| </p> | |||
| <h3>Solution</h3> | |||
| <p> | |||
| The motion of particle is accelerated by electric field, so | |||
| $$d = vt-\frac{at^2}{2} \;(1)$$ | |||
| Applying Newton Second Law | |||
| $$F = qE = ma$$ | |||
| then, | |||
| $$a = \frac{qE}{m} \;(2)$$ | |||
| Putting $(2)$ into $(1)$ | |||
| $$\boxed{E = 2m\frac{d-vt}{qt^2}}$$ | |||
| </p> | |||
| <p style="text-align: right; font-style: italic; font-size: 14;"> | |||
| BSc. Luis Daniel Fernández Quintana<br> | |||
| Physics Department (FCNE)<br> | |||
| Universidad de Oriente, Cuba<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> | |||
| </body> | |||
| </html> | |||