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Two metal spheres (radii r1,r2 with r1<r2) are very far apart but are connected by a thin wire. If their combined charge is Q, then what is their common Potential? |
Answer» <p>Two metal spheres (radii <span class="mjx-chtml" id="MathJax-Element-1-Frame"><span class="mjx-math" id="MJXc-Node-200895"><span class="mjx-mrow" id="MJXc-Node-200896"><span class="mjx-msubsup" id="MJXc-Node-200897"><span class="mjx-base"><span class="mjx-mi" id="MJXc-Node-200898"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">r</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" id="MJXc-Node-200899" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo" id="MJXc-Node-200900"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-msubsup MJXc-space1" id="MJXc-Node-200901"><span class="mjx-base"><span class="mjx-mi" id="MJXc-Node-200902"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">r</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" id="MJXc-Node-200903" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span> with <span class="mjx-chtml" id="MathJax-Element-2-Frame"><span class="mjx-math" id="MJXc-Node-200904"><span class="mjx-mrow" id="MJXc-Node-200905"><span class="mjx-msubsup" id="MJXc-Node-200906"><span class="mjx-base"><span class="mjx-mi" id="MJXc-Node-200907"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">r</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" id="MJXc-Node-200908" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo MJXc-space3" id="MJXc-Node-200909"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;"><</span></span><span class="mjx-msubsup MJXc-space3" id="MJXc-Node-200910"><span class="mjx-base"><span class="mjx-mi" id="MJXc-Node-200911"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">r</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" id="MJXc-Node-200912" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span>) are very far apart but are connected by a thin wire. If their combined charge is <span class="mjx-chtml" id="MathJax-Element-3-Frame"><span class="mjx-math" id="MJXc-Node-200913"><span class="mjx-mrow" id="MJXc-Node-200914"><span class="mjx-mi" id="MJXc-Node-200915"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.446em;">Q</span></span></span></span></span>, then what is their common Potential?<br></p> | |