Added Luis's English solution of 10.2.8
en/10.2.8.md
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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"> | ||
| + | <script async src="https://www.googletagmanager.com/gtag/js?id=G-DDMB38YMLD"></script> | ||
| + | |||
| + | <title>Savchenko Solutions</title> | ||
| + | <meta property="og:image" content="img/logo.png"> | ||
| + | <meta property="og:title" content="Savchenko Solutions"/> | ||
| + | <meta name="description" | ||
| + | content="A website with solutions to physics problems from Savenko Textbook" /> | ||
| + | <meta name="keywords" content="physics, olympiads, ipho, savchenko" /> | ||
| + | <link rel="stylesheet" href="https://savchenko-physics.github.io/css/css-latex/style.css" /> | ||
| + | <link rel="icon" type="image/x-icon" href="https://savchenko-physics.github.io/img/favicon.ico"> | ||
| + | </head> | ||
| + | |||
| + | <body id="top"> | ||
| + | <header> | ||
| + | <h2>Solutions of Savchenko Physics Textbook</h2> | ||
| + | <p class="author"> | ||
| + | Aliaksandr Melnichenka <br/> | ||
| + | October 2023 | ||
| + | </p> | ||
| + | </header> | ||
| + | |||
| + | <main> | ||
| + | <article> | ||
| + | <h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3> | ||
| + | |||
| + | <h4>Statement</h4> | ||
| + | <p> | ||
| + | $10.2.8$ | ||
| + | A plane capacitor is placed in a homogeneous magnetic field od induction $B$ parallel to the plates. From point A, electrons enter perpendicularly to magnetic field direction. The tension (voltage) applied to the plates is $V$. What is the condition for which electrons pass through the capacitor? | ||
| + | </p> | ||
| + | <center> | ||
| + | <figure> | ||
| + | <img src="statement.png" | ||
| + | loading="lazy" alt="10.2.8" width="300" /> | ||
| + | <figcaption> | ||
| + | For problem 10.2.8 | ||
| + | </figcaption> | ||
| + | </figure> | ||
| + | </center> | ||
| + | <h4>Solution</h4> | ||
| + | <p class="TxtSolutions"> | ||
| + | Electrons pass through capacitor if they don't collide with plates. So, supposing a capacitor of infinite length, electron's velocity must be parallel to the plates (or its horizontal range over a plate greater than its enter's height). This is possible if electric and magnetic forces are in equilibrium (equal absolute values and opposed directions). | ||
| + | </p> | ||
| + | <center> | ||
| + | $evB = eE$ | ||
| + | </center> | ||
| + | <center> | ||
| + | $v = \frac{E}{B}$ | ||
| + | </center> | ||
| + | <p calss="TxtSolutions"> | ||
| + | As $E=\frac{V}{h}$, | ||
| + | </p> | ||
| + | <center> | ||
| + | $\boxed{v = \frac{V}{Bh}}$ | ||
| + | </center> | ||
| + | <p class="TxtSolutions"> | ||
| + | This device is known as speed's selector. | ||
| + | </p> | ||
| + | <p class="TxtSolutions" 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> | ||
| + | </article> | ||
| + | </main> | ||
| + | |||
| + | <script> | ||
| + | MathJax = { | ||
| + | tex: { | ||
| + | inlineMath: [['$', '$'],], | ||
| + | }, | ||
| + | } | ||
| + | const typeFaceToggle = document.getElementById('typeface-toggle') | ||
| + | const typeface = document.getElementById('typeface') | ||
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| + | typeface.textContent = document.body.classList.contains('libertinus') ? 'Libertinus' : 'Latin Modern' | ||
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| + | |||
| + | const darkModeToggle = document.getElementById('dark-mode-toggle') | ||
| + | darkModeToggle.addEventListener('click', () => { | ||
| + | document.body.classList.toggle('latex-dark') | ||
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| + | </script> | ||
| + | <script> | ||
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| + | <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> | ||
| + | |||
| + | </body> | ||
| + | |||
| + | </html> | ||
| @@ -0,0 +1,104 @@ | |||
| <!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"> | |||
| <script async src="https://www.googletagmanager.com/gtag/js?id=G-DDMB38YMLD"></script> | |||
| <title>Savchenko Solutions</title> | |||
| <meta property="og:image" content="img/logo.png"> | |||
| <meta property="og:title" content="Savchenko Solutions"/> | |||
| <meta name="description" | |||
| content="A website with solutions to physics problems from Savenko Textbook" /> | |||
| <meta name="keywords" content="physics, olympiads, ipho, savchenko" /> | |||
| <link rel="stylesheet" href="https://savchenko-physics.github.io/css/css-latex/style.css" /> | |||
| <link rel="icon" type="image/x-icon" href="https://savchenko-physics.github.io/img/favicon.ico"> | |||
| </head> | |||
| <body id="top"> | |||
| <header> | |||
| <h2>Solutions of Savchenko Physics Textbook</h2> | |||
| <p class="author"> | |||
| Aliaksandr Melnichenka <br/> | |||
| October 2023 | |||
| </p> | |||
| </header> | |||
| <main> | |||
| <article> | |||
| <h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3> | |||
| <h4>Statement</h4> | |||
| <p> | |||
| $10.2.8$ | |||
| A plane capacitor is placed in a homogeneous magnetic field od induction $B$ parallel to the plates. From point A, electrons enter perpendicularly to magnetic field direction. The tension (voltage) applied to the plates is $V$. What is the condition for which electrons pass through the capacitor? | |||
| </p> | |||
| <center> | |||
| <figure> | |||
| <img src="statement.png" | |||
| loading="lazy" alt="10.2.8" width="300" /> | |||
| <figcaption> | |||
| For problem 10.2.8 | |||
| </figcaption> | |||
| </figure> | |||
| </center> | |||
| <h4>Solution</h4> | |||
| <p class="TxtSolutions"> | |||
| Electrons pass through capacitor if they don't collide with plates. So, supposing a capacitor of infinite length, electron's velocity must be parallel to the plates (or its horizontal range over a plate greater than its enter's height). This is possible if electric and magnetic forces are in equilibrium (equal absolute values and opposed directions). | |||
| </p> | |||
| <center> | |||
| $evB = eE$ | |||
| </center> | |||
| <center> | |||
| $v = \frac{E}{B}$ | |||
| </center> | |||
| <p calss="TxtSolutions"> | |||
| As $E=\frac{V}{h}$, | |||
| </p> | |||
| <center> | |||
| $\boxed{v = \frac{V}{Bh}}$ | |||
| </center> | |||
| <p class="TxtSolutions"> | |||
| This device is known as speed's selector. | |||
| </p> | |||
| <p class="TxtSolutions" 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> | |||
| </article> | |||
| </main> | |||
| <script> | |||
| MathJax = { | |||
| tex: { | |||
| inlineMath: [['$', '$'],], | |||
| }, | |||
| } | |||
| const typeFaceToggle = document.getElementById('typeface-toggle') | |||
| const typeface = document.getElementById('typeface') | |||
| typeFaceToggle.addEventListener('click', () => { | |||
| document.body.classList.toggle('libertinus') | |||
| typeface.textContent = document.body.classList.contains('libertinus') ? 'Libertinus' : 'Latin Modern' | |||
| }) | |||
| const darkModeToggle = document.getElementById('dark-mode-toggle') | |||
| darkModeToggle.addEventListener('click', () => { | |||
| document.body.classList.toggle('latex-dark') | |||
| }) | |||
| </script> | |||
| <script> | |||
| window.dataLayer = window.dataLayer || []; | |||
| function gtag(){dataLayer.push(arguments);} | |||
| gtag('js', new Date()); | |||
| gtag('config', 'G-DDMB38YMLD'); | |||
| </script> | |||
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| </body> | |||
| </html> | |||