AST101H1 Study Guide - Midterm Guide: 3 Ft Gauge Rail Modelling, Fifth Normal Form

<p>Two spherical shells have a common center. A -1.00x10^-6 C charge is spread uniformly over theinner shell, which has a radius of 0.050 m. A +5.50x10^-6 C charge is spread uniformly over theouter shell, which has a radius of 0.15 m. Find the magnitude anddirection of the electric field at a distance (measured from thecommon center) of <br /><strong>(a)</strong> 0.20m,<br /><em>E</em> = <inputname="resp_num_c18go_tutorial_1_60_1" type="text"/>&#160;<selectname="resp_str_c18go_tutorial_1_60_2"><optionselected="selected">&#160;</option><optionvalue="resp_3">C/N</option><optionvalue="resp_2">N</option><optionvalue="resp_0">N/C</option><optionvalue="resp_1">C</option></select>&#160;<selectname="resp_str_c18go_tutorial_1_60_3"><optionselected="selected">&#160;</option><optionvalue="resp_0">radially outward</option><optionvalue="resp_2">no direction</option><optionvalue="resp_1">radiallyinward</option></select><br/><strong>(b)</strong> 0.10 m, <br/><em>E</em> = <inputname="resp_num_c18go_tutorial_1_60_4" type="text"/>&#160;<selectname="resp_str_c18go_tutorial_1_60_5"><optionselected="selected">&#160;</option><optionvalue="resp_2">N</option><optionvalue="resp_3">C/N</option><optionvalue="resp_0">N/C</option><optionvalue="resp_1">C</option></select>&#160;<selectname="resp_str_c18go_tutorial_1_60_6"><optionselected="selected">&#160;</option><optionvalue="resp_1">radially outward</option><optionvalue="resp_0">radially inward</option><optionvalue="resp_2">no direction</option></select><br/><strong>(c)</strong> 0.025 m.<br/><em>E</em> = <inputname="resp_num_c18go_tutorial_1_60_7" type="text"/>&#160;<selectname="resp_str_c18go_tutorial_1_60_8"><optionselected="selected">&#160;</option><optionvalue="resp_0">N/C</option><optionvalue="resp_2">N</option><optionvalue="resp_3">C/N</option><optionvalue="resp_1">C</option></select>&#160;<selectname="resp_str_c18go_tutorial_1_60_9"><optionselected="selected">&#160;</option><optionvalue="resp_2">radially inward</option><optionvalue="resp_1">radially outward</option><optionvalue="resp_0">nodirection</option></select></p>
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<p>A one dimensional harmonic oscillator is changed by the addition of another force so that V= (b/x²) + &#189; m&#969;²x². One resulting wave function is &#968;= Ax^ne^{-ax^2}&#160;and d²&#968;/dx² =[n(n-1)/x²&#8211; 2a(2n+1) + 4a²x²]&#968;. Evaluate a and find E in terms of b, h and &#969;.</p>

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<div id="tallPI"class="problemIntroduction">A&#160;<span>0.32</span>&#160;<imgsrc="http://session.masteringphysics.com/render?units=%5Cmu+C"alt="\mu C" align="middle" />&#160;particle moves with aspeed of&#160;<span>17</span>&#160;<imgsrc="http://session.masteringphysics.com/render?units=m%2Fs"alt="m/s" align="middle" />through a region where the magneticfield has a strengthof&#160;<span>0.95</span>&#160;<imgsrc="http://session.masteringphysics.com/render?units=T" alt="T"align="middle" />.</div>
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<div class="partText">At what angle to the field is theparticle moving if the force exerted on it is&#160;<imgsrc="http://session.masteringphysics.com/render?tex=4.8%5Ctimes+10%5E%7B-6%7D%7B%5Crm+N%7D"alt="4.8\times 10^{-6}{\rm N}" align="middle"/>?</div>
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<div class="partText">At what angle to the field is theparticle moving if the force exerted on it is&#160;<imgsrc="http://session.masteringphysics.com/render?tex=3.0%5Ctimes+10%5E%7B-6%7D%7B%5Crm+N%7D"alt="3.0\times 10^{-6}{\rm N}" align="middle"/>?</div>
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<div class="partText">At what angle to the field is theparticle moving if the force exerted on it is&#160;<imgsrc="http://session.masteringphysics.com/render?tex=1.0%5Ctimes+10%5E%7B-7%7D%7B%5Crm+N%7D"alt="1.0\times 10^{-7}{\rm N}" align="middle"/>?</div>
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