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A magnet of length L and magnetic moment M is made into two halves A and B, perpendicular to its axis. One piece A is bent into a semicircle of radius R and is joined to the other piece at the poles as shown in the figure below. Assuming that the magnet is in the form of a thin wire initially .Find the magnetic moment of the resulting magnet. |
Answer» <p>A magnet of length <span class="mjx-chtml" id="MathJax-Element-1-Frame"><span class="mjx-math" id="MJXc-Node-305190"><span class="mjx-mrow" id="MJXc-Node-305191"><span class="mjx-mi" id="MJXc-Node-305192"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">L</span></span></span></span></span> and magnetic moment <span class="mjx-chtml" id="MathJax-Element-2-Frame"><span class="mjx-math" id="MJXc-Node-305193"><span class="mjx-mrow" id="MJXc-Node-305194"><span class="mjx-mi" id="MJXc-Node-305195"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.081em;">M</span></span></span></span></span> is made into two halves <span class="mjx-chtml" id="MathJax-Element-3-Frame"><span class="mjx-math" id="MJXc-Node-305196"><span class="mjx-mrow" id="MJXc-Node-305197"><span class="mjx-mi" id="MJXc-Node-305198"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span> and <span class="mjx-chtml" id="MathJax-Element-4-Frame"><span class="mjx-math" id="MJXc-Node-305199"><span class="mjx-mrow" id="MJXc-Node-305200"><span class="mjx-mi" id="MJXc-Node-305201"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span></span></span></span>, perpendicular to its axis. One piece <span class="mjx-chtml" id="MathJax-Element-5-Frame"><span class="mjx-math" id="MJXc-Node-305202"><span class="mjx-mrow" id="MJXc-Node-305203"><span class="mjx-mi" id="MJXc-Node-305204"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span> is bent into a semicircle of radius <span class="mjx-chtml" id="MathJax-Element-6-Frame"><span class="mjx-math" id="MJXc-Node-305205"><span class="mjx-mrow" id="MJXc-Node-305206"><span class="mjx-mi" id="MJXc-Node-305207"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span></span></span></span> and is joined to the other piece at the poles as shown in the figure below. Assuming that the magnet is in the form of a thin wire initially .Find the magnetic moment of the resulting magnet.<br><br><br><br><br><br><img alt="" height="99" src="https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1341957/original_17.qstn.png" width="227"> <br></p> | |