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en/9.1.5.md
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| + | <meta name="author" content="Aliaksandr Melnichenka"> | ||
| + | <meta name="date" content="2023-10" scheme="YYYY-MM"> | ||
| + | <meta property="og:title" content="A conductor of mass 0.16 kg and length 80 cm is suspended horizontally in a vertical uniform magnetic field on two thin threads. The ends of the conductor are connected to a current source by flexible wires located outside the field. Find the angle by which the suspension threads deviate from the vertical if a current of 2 A flows through the conductor and the magnetic field induction is 1 T."> | ||
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| + | <meta property="og:description" content="A conductor of mass 0.16 kg and length 80 cm is suspended horizontally in a vertical uniform magnetic field on two thin threads. The ends of the conductor are connected to a current source by flexible wires located outside the field. Find the angle by which the suspension threads deviate from the vertical if a current of 2 A flows through the conductor and the magnetic field induction is 1 T."> | ||
| + | <meta name="yandex-verification" content="6cfda41f74038368"> | ||
| + | <title>A conductor of mass 0.16 kg and length 80 cm is suspended horizontally in a vertical uniform magnetic field on two thin threads. The ends of the conductor are connected to a current source by flexible wires located outside the field. Find the angle by which the suspension threads deviate from the vertical if a current of 2 A flows through the conductor and the magnetic field induction is 1 T.</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> | ||
| + | $9.1.5.$ A conductor of mass $0.16$ kg and length $80$ cm is suspended horizontally in a vertical uniform magnetic field on two thin threads. The ends of the conductor are connected to a current source by flexible wires located outside the field. Find the angle by which the suspension threads deviate from the vertical if a current of $2$ A flows through the conductor and the magnetic field induction is $1$ T. | ||
| + | </p> | ||
| + | |||
| + | <h3>Solution</h3> | ||
| + | <p> | ||
| + | |||
| + | </p> | ||
| + | <center> | ||
| + | <figure> | ||
| + | <img src="https://savchenkosolutions.com/9/9.1.5/9.1.5_1.png" | ||
| + | loading="lazy" width="150" /> | ||
| + | <figcaption> | ||
| + | Forces acting on the system | ||
| + | </figcaption> | ||
| + | </figure> | ||
| + | </center> | ||
| + | <p> | ||
| + | Ampere force acting on a conductor | ||
| + | $$ F = Il\cdot B $$ | ||
| + | From Newton's second law, the condition of equilibrium on the horizontal and vertical axes | ||
| + | $$ T\cos\alpha = mg;\quad T\sin\alpha = F $$ | ||
| + | dividing one expression by the other, we get | ||
| + | $$ \tan\alpha = \frac{F}{mg} $$ | ||
| + | $$ \boxed{\alpha = \arctan \left(\frac{IlB}{mg}\right) = 45^{\circ}} $$ | ||
| + | |||
| + | |||
| + | </p> | ||
| + | |||
| + | <h4>Answer: $\alpha = 45^{\circ}$</h4> | ||
| + | <p style="text-align: right; font-style: italic; font-size: 14;"> | ||
| + | Andrei Yersh<br> | ||
| + | </p> | ||
| + | |||
| + | |||
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| + | <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> | ||
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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"> | |||
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| <meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda"> | |||
| <meta name="description" content="A conductor of mass 0.16 kg and length 80 cm is suspended horizontally in a vertical uniform magnetic field on two thin threads. The ends of the conductor are connected to a current source by flexible wires located outside the field. Find the angle by which the suspension threads deviate from the vertical if a current of 2 A flows through the conductor and the magnetic field induction is 1 T."> | |||
| <meta name="author" content="Aliaksandr Melnichenka"> | |||
| <meta name="date" content="2023-10" scheme="YYYY-MM"> | |||
| <meta property="og:title" content="A conductor of mass 0.16 kg and length 80 cm is suspended horizontally in a vertical uniform magnetic field on two thin threads. The ends of the conductor are connected to a current source by flexible wires located outside the field. Find the angle by which the suspension threads deviate from the vertical if a current of 2 A flows through the conductor and the magnetic field induction is 1 T."> | |||
| <meta property="og:image" content="img/logo.png"> | |||
| <meta property="og:description" content="A conductor of mass 0.16 kg and length 80 cm is suspended horizontally in a vertical uniform magnetic field on two thin threads. The ends of the conductor are connected to a current source by flexible wires located outside the field. Find the angle by which the suspension threads deviate from the vertical if a current of 2 A flows through the conductor and the magnetic field induction is 1 T."> | |||
| <meta name="yandex-verification" content="6cfda41f74038368"> | |||
| <title>A conductor of mass 0.16 kg and length 80 cm is suspended horizontally in a vertical uniform magnetic field on two thin threads. The ends of the conductor are connected to a current source by flexible wires located outside the field. Find the angle by which the suspension threads deviate from the vertical if a current of 2 A flows through the conductor and the magnetic field induction is 1 T.</title> | |||
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| }, | |||
| showProcessingMessages: false, | |||
| messageStyle: 'none' | |||
| }); | |||
| </script> | |||
| </head> | |||
| <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> | |||
| $9.1.5.$ A conductor of mass $0.16$ kg and length $80$ cm is suspended horizontally in a vertical uniform magnetic field on two thin threads. The ends of the conductor are connected to a current source by flexible wires located outside the field. Find the angle by which the suspension threads deviate from the vertical if a current of $2$ A flows through the conductor and the magnetic field induction is $1$ T. | |||
| </p> | |||
| <h3>Solution</h3> | |||
| <p> | |||
| </p> | |||
| <center> | |||
| <figure> | |||
| <img src="https://savchenkosolutions.com/9/9.1.5/9.1.5_1.png" | |||
| loading="lazy" width="150" /> | |||
| <figcaption> | |||
| Forces acting on the system | |||
| </figcaption> | |||
| </figure> | |||
| </center> | |||
| <p> | |||
| Ampere force acting on a conductor | |||
| $$ F = Il\cdot B $$ | |||
| From Newton's second law, the condition of equilibrium on the horizontal and vertical axes | |||
| $$ T\cos\alpha = mg;\quad T\sin\alpha = F $$ | |||
| dividing one expression by the other, we get | |||
| $$ \tan\alpha = \frac{F}{mg} $$ | |||
| $$ \boxed{\alpha = \arctan \left(\frac{IlB}{mg}\right) = 45^{\circ}} $$ | |||
| </p> | |||
| <h4>Answer: $\alpha = 45^{\circ}$</h4> | |||
| <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> | |||