Translated 9.1.6-9.1.15
en/9.1.13.md
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| + | <title>A coil with a current flowing through its turns stands vertically on a plane. The total weight of the coil is P, the number of turns is n, the radius is R, and the current in the turns is I. At what induction of a uniform magnetic field directed horizontally will the coil overturn under the action of this field?</title> | ||
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| + | Solutions of Savchenko Problems in Physics <br> | ||
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| + | <h3 id="back-link"><a href="../../#9.1">$\leftarrow$Back</a></h3> | ||
| + | |||
| + | <h3> Statement </h3> | ||
| + | <p> | ||
| + | $9.1.13^*.$ A coil with a current flowing through its turns stands vertically on a plane. The total weight of the coil is $P$, the number of turns is $n$, the radius is $R$, and the current in the turns is $I$. At what induction of a uniform magnetic field directed horizontally will the coil overturn under the action of this field? | ||
| + | </p> | ||
| + | |||
| + | <h3>Solution</h3> | ||
| + | <p> | ||
| + | Moment of gravity for the coil relative to the edge of the coil: | ||
| + | $$ M_{mg} = R\cdot mg = PR $$ | ||
| + | Moment of magnetic field forces: | ||
| + | $$ M_B = n\cdot BSI = n\cdot \pi R^2BI $$ | ||
| + | In the equilibrium condition, the total moment of forces, taking into account the signs, is equal to zero | ||
| + | $$ n\cdot \pi R^2BI = PR \Rightarrow \boxed{ B = \frac{P}{n\pi RI}} $$ | ||
| + | |||
| + | </p> | ||
| + | |||
| + | <h4>Answer</h4> | ||
| + | <p> | ||
| + | $$B = \frac{P}{n\pi RI}$$ | ||
| + | </p> | ||
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| <meta name="date" content="2023-10" scheme="YYYY-MM"> | |||
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| <title>A coil with a current flowing through its turns stands vertically on a plane. The total weight of the coil is P, the number of turns is n, the radius is R, and the current in the turns is I. At what induction of a uniform magnetic field directed horizontally will the coil overturn under the action of this field?</title> | |||
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| <body style=""> | |||
| <header style="text-align:center;"> | |||
| <a href="../../" style="text-decoration: none;"> | |||
| <div id="logo"> | |||
| <span><img src="../../img/book.png"></span><span>Savchenko Solutions</span> | |||
| </div> | |||
| </a> | |||
| <p class="author"> | |||
| Solutions of Savchenko Problems in Physics <br> | |||
| <i><b>knowledge must be free</b></i> | |||
| </p> | |||
| </header> | |||
| <h3 id="back-link"><a href="../../#9.1">$\leftarrow$Back</a></h3> | |||
| <h3> Statement </h3> | |||
| <p> | |||
| $9.1.13^*.$ A coil with a current flowing through its turns stands vertically on a plane. The total weight of the coil is $P$, the number of turns is $n$, the radius is $R$, and the current in the turns is $I$. At what induction of a uniform magnetic field directed horizontally will the coil overturn under the action of this field? | |||
| </p> | |||
| <h3>Solution</h3> | |||
| <p> | |||
| Moment of gravity for the coil relative to the edge of the coil: | |||
| $$ M_{mg} = R\cdot mg = PR $$ | |||
| Moment of magnetic field forces: | |||
| $$ M_B = n\cdot BSI = n\cdot \pi R^2BI $$ | |||
| In the equilibrium condition, the total moment of forces, taking into account the signs, is equal to zero | |||
| $$ n\cdot \pi R^2BI = PR \Rightarrow \boxed{ B = \frac{P}{n\pi RI}} $$ | |||
| </p> | |||
| <h4>Answer</h4> | |||
| <p> | |||
| $$B = \frac{P}{n\pi RI}$$ | |||
| </p> | |||
| <p style="text-align: right; font-style: italic; font-size: 14;"> | |||
| Andrei Yersh<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> alex@savchenkosolutions.com <br></small> | |||
| </p> | |||
| </footer> | |||
| </body> | |||
| </html> | |||