Translated 9.2.1-9.2.9
en/9.2.4.md
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| + | <span><img src="../../img/book.png"></span><span>Savchenko Solutions</span> | ||
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| + | Solutions of Savchenko Problems in Physics <br> | ||
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| + | <h3 id="back-link"><a href="../../#9.2">$\leftarrow$Back</a></h3> | ||
| + | |||
| + | <h3> Statement </h3> | ||
| + | <p> | ||
| + | $9.2.4.$ A force of $2.5\cdot 10^{-7}$ N acts on a unit of length of a straight long wire with current from the side of a second wire with the same current. The distance between the wires is $1$ m, the current in the wires is 1 A. What is the magnetic permeability of this medium? | ||
| + | </p> | ||
| + | |||
| + | <h3>Solution</h3> | ||
| + | <p> | ||
| + | Magnetic induction of one wire with current $I$ | ||
| + | $$ B = \frac{\mu_0 \mu I}{2\pi R} $$ | ||
| + | The force acting from the magnetic field $B$ on a piece of wire $\Delta l$ with a current of $I$ | ||
| + | $$ F = BI\Delta l = \frac{\mu_0 \mu I^2 \Delta l }{2\pi R} $$ | ||
| + | Where do we express the magnetic permeability of the medium? | ||
| + | $$ \boxed{\mu = \frac{2\pi F R}{\mu_0 I^2 \Delta l } = 1.25} $$ | ||
| + | |||
| + | </p> | ||
| + | |||
| + | <h4>Answer</h4> | ||
| + | <p> | ||
| + | $$\mu = 1.25$$ | ||
| + | </p> | ||
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| <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="../../#9.2">$\leftarrow$Back</a></h3> | |||
| <h3> Statement </h3> | |||
| <p> | |||
| $9.2.4.$ A force of $2.5\cdot 10^{-7}$ N acts on a unit of length of a straight long wire with current from the side of a second wire with the same current. The distance between the wires is $1$ m, the current in the wires is 1 A. What is the magnetic permeability of this medium? | |||
| </p> | |||
| <h3>Solution</h3> | |||
| <p> | |||
| Magnetic induction of one wire with current $I$ | |||
| $$ B = \frac{\mu_0 \mu I}{2\pi R} $$ | |||
| The force acting from the magnetic field $B$ on a piece of wire $\Delta l$ with a current of $I$ | |||
| $$ F = BI\Delta l = \frac{\mu_0 \mu I^2 \Delta l }{2\pi R} $$ | |||
| Where do we express the magnetic permeability of the medium? | |||
| $$ \boxed{\mu = \frac{2\pi F R}{\mu_0 I^2 \Delta l } = 1.25} $$ | |||
| </p> | |||
| <h4>Answer</h4> | |||
| <p> | |||
| $$\mu = 1.25$$ | |||
| </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> | |||
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