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<p>This week we introduce magnetic fields! In this lesson we start with a reminder of our everyday interaction with magnetic fields, and then disucss how moving charges are affected by magnetic fields.</p>
<p>Textbook Links</p>
<ul>
<li><a href="https://openlearninglibrary.mit.edu/courses/course-v1:MITx+8.02.2x+2T2018/pdfbook/0/#viewer-frame" target="[object Object]">Chapter 8.1-8.2, 8.5: Magnetic Fields, Charged Particles in Magnetic Fields</a></li>
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<h2 class="hd hd-2 unit-title">L17v1a: Introduction to Magnetic Fields</h2>
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<h3 class="hd hd-2">L17v01a: Introduction to Magnetic Fields</h3>
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<h2 class="hd hd-2 unit-title">L17Q1: North Pole, South Pole</h2>
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In the figure below a drawing of the magnetic field lines outside of a bar magnet is shown. </p>
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Which of the following statements is (are) true. Check all that applied. </p>
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<text>3. The south pole of the Earth's magnetic field is in or near Antartica.</text>
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<h2 class="hd hd-2 unit-title">Review: Cross Products</h2>
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<p><b>Notation</b></p><p>A vector perpendicular to the plane of the screen is represented by a circle. If the vector is out of the plane of the screen there is a dot inside the circle. If the vector is into the screen there is a cross inside the circle.</p><center><img src="/assets/courseware/v1/ed81b3d7036915cece9f6dfd3f036800/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_html_lesson17_01.svg" width="250"/></center><center><p><b> Unit vectors</b></p></center><p><u>Cartesian coordinate system</u>: The unit vector \(\hat{k}\) is obtained as \(\hat{k}=\hat{i}\times \hat{j}\), therefore if the unit vectors \(\hat{i}\) and \(\hat{j}\) are in the plane of the screen then \(\hat{k}\) is out of the screen.</p><p><u>Cylindrical coordinate system</u>: The unit vector \(\hat{k}\) is obtained as \(\hat{k}=\hat{r}\times \hat{\theta}\), therefore if the unit vectors \(\hat{r}\) and \(\hat{\theta}\) are in the plane of the screen, then \(\hat{k}\) is out of the screen.</p><center><img src="/assets/courseware/v1/a4b2e68923867c4a839be53a2faa3d00/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_html_lesson17_01_b.svg" width="400"/></center>
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<h2 class="hd hd-2 unit-title">L17Q2: Direction of the Magnetic Force</h2>
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Direction of the Magnetic Force
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Indicate the direction of the forces exerted by the magnetic field on the moving charges at the instant shown in the figures above. Express your answer in terms of hati for [mathjaxinline]\hat{i}[/mathjaxinline], hatj for [mathjaxinline]\hat{j}[/mathjaxinline], and hatk for [mathjaxinline]\hat{k}[/mathjaxinline]. Enter zero if there is no force on the charge. Include the negative sign in front of the unit vector as needed, example -hati for [mathjaxinline]-\hat{i}[/mathjaxinline]. </p>
<p><b class="bfseries">1.</b> The direction of the magnetic force experienced by charge 1 is: </p>
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<p><b class="bfseries">2.</b> The direction of the magnetic force experienced by charge 2 is: </p>
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<p><b class="bfseries">3.</b> The direction of the magnetic force experienced by charge 3 is: </p>
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<p><b class="bfseries">4.</b> The direction of the magnetic force experienced by charge 4 is: </p>
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Direction of the Magnetic Force, part 2.
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A charged object is moving in a region in space with a magnetic field [mathjaxinline]\vec{B}[/mathjaxinline]. There is no other force acting on the object. As a result, the particle's path is a circle of radius [mathjaxinline]R[/mathjaxinline]. Determine the direction of the magnetic field. Express your answer in terms of hatr for [mathjaxinline]\hat{r}[/mathjaxinline], hattheta for [mathjaxinline]\hat{\theta }[/mathjaxinline], and hatk for [mathjaxinline]\hat{k}[/mathjaxinline]. Include the negative sign in front of the unit vector as needed, example -hatr for [mathjaxinline]-\hat{r}[/mathjaxinline]. </p>
<p><b class="bfseries">Figure 1.</b> The direction of [mathjaxinline]\vec{B}[/mathjaxinline] is: </p>
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<p><b class="bfseries">Figure 2.</b> The direction of [mathjaxinline]\vec{B}[/mathjaxinline] is: </p>
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<h2 class="hd hd-2 unit-title">L17v3: Worked Example - Velocity Selector</h2>
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Velocity Selector
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Electrons with charge [mathjaxinline]-e[/mathjaxinline] and mass [mathjaxinline]m[/mathjaxinline] are emitted from the cathode <b class="bfseries">C</b> and accelerated toward slit <b class="bfseries">A</b> with different speeds in the direction shown. The electrons enter a region with a downward pointing electric field (magnitude [mathjaxinline]E[/mathjaxinline]) and a magnetic field (magnitude [mathjaxinline]B[/mathjaxinline]) that points into the plane of the figure. Gravity can be ignored in this case. The electrons that travel on a straight trajectory through the gap between the plates have speed </p>
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<h3 class="hd hd-2">L17v03: Worked Example - Velocity Selector</h3>
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Motion of a Charged Particle in a Uniform Magnetic Field
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Two charged particles of identical charge move in circular orbits in the same uniform magnetic field [mathjaxinline]\vec{\mathbf{B}}=B_ o\hat{\mathbf{k}}[/mathjaxinline]. Particle 1 has twice the speed of particle 2, [mathjaxinline]v_1=2v_2[/mathjaxinline]. Particle 2 has four times the mass of particle 1, [mathjaxinline]m_2=4m_1[/mathjaxinline]. </p>
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