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<meta name="description" content="An electron rotates in an orbit of radius $R$ around a proton. How will the frequency of rotation of an electron in the same orbit change if the system is placed in a weak magnetic field of induction $B$, directed along the axis of rotation?">
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<meta property="og:title" content="An electron rotates in an orbit of radius $R$ around a proton. How will the frequency of rotation of an electron in the same orbit change if the system is placed in a weak magnetic field of induction $B$, directed along the axis of rotation?">
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<meta property="og:description" content="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?">
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<meta property="og:description" content="An electron rotates in an orbit of radius $R$ around a proton. How will the frequency of rotation of an electron in the same orbit change if the system is placed in a weak magnetic field of induction $B$, directed along the axis of rotation?">
<title>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?</title>
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<title>An electron rotates in an orbit of radius $R$ around a proton. How will the frequency of rotation of an electron in the same orbit change if the system is placed in a weak magnetic field of induction $B$, directed along the axis of rotation?</title>
An electron rotates in an orbit of radius $R$ around a proton. How will the frequency of rotation of an electron in the same orbit change if the system is placed in a weak magnetic field of induction $B$, directed along the axis of rotation?
</p>
<h3>Solution</h3>
<p>
Without magnetic field, electrical force is equivalent to centripetal force:
Now, it's time to check the orders of each magnitude. Let's see the terms under square root. Let's consider $e \approx 10^{-19}{\rm{C}}$, $B \approx 10^{-6} T$ (due to problem refers to weak magnetic field, we take in account the order of Earth's magnetic field from Problem 10.1.2), $m_e \approx 10^{-31}{\rm{kg}}$ and $R \approx 10^{-10}{\rm{m}}$ (in the order of Å). Hence,
<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>
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="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?">
<meta name="description" content="An electron rotates in an orbit of radius $R$ around a proton. How will the frequency of rotation of an electron in the same orbit change if the system is placed in a weak magnetic field of induction $B$, directed along the axis of rotation?">
<meta property="og:title" content="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?">
<meta property="og:title" content="An electron rotates in an orbit of radius $R$ around a proton. How will the frequency of rotation of an electron in the same orbit change if the system is placed in a weak magnetic field of induction $B$, directed along the axis of rotation?">
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<meta property="og:description" content="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?">
<meta property="og:description" content="An electron rotates in an orbit of radius $R$ around a proton. How will the frequency of rotation of an electron in the same orbit change if the system is placed in a weak magnetic field of induction $B$, directed along the axis of rotation?">
<title>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?</title>
<title>An electron rotates in an orbit of radius $R$ around a proton. How will the frequency of rotation of an electron in the same orbit change if the system is placed in a weak magnetic field of induction $B$, directed along the axis of rotation?</title>
An electron rotates in an orbit of radius $R$ around a proton. How will the frequency of rotation of an electron in the same orbit change if the system is placed in a weak magnetic field of induction $B$, directed along the axis of rotation?
An electron rotates in an orbit of radius $R$ around a proton. How will the frequency of rotation of an electron in the same orbit change if the system is placed in a weak magnetic field of induction $B$, directed along the axis of rotation?
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
Without magnetic field, electrical force is equivalent to centripetal force:
Without magnetic field, electrical force is equivalent to centripetal force:
Now, it's time to check the orders of each magnitude. Let's see the terms under square root. Let's consider $e \approx 10^{-19}{\rm{C}}$, $B \approx 10^{-6} T$ (due to problem refers to weak magnetic field, we take in account the order of Earth's magnetic field from Problem 10.1.2), $m_e \approx 10^{-31}{\rm{kg}}$ and $R \approx 10^{-10}{\rm{m}}$ (in the order of Å). Hence,
Now, it's time to check the orders of each magnitude. Let's see the terms under square root. Let's consider $e \approx 10^{-19}{\rm{C}}$, $B \approx 10^{-6} T$ (due to problem refers to weak magnetic field, we take in account the order of Earth's magnetic field from Problem 10.1.2), $m_e \approx 10^{-31}{\rm{kg}}$ and $R \approx 10^{-10}{\rm{m}}$ (in the order of Å). Hence,
<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>
<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>
