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<p> This week we start exploring how charge behaves in insulators and conductors. Up until now, most of the problems have dealt implicitly with insulators, and in this lesson we see how charge moves in a conductor in electrostatic equilibrium.</p><p> Textbook Links </p><ul><li><a href="/courses/course-v1:MITx+8.02.1x+1T2019/pdfbook/0/chapter/3/17">Chapter 3.3-3.4 Conductors</a></li><li><a href="/courses/course-v1:MITx+8.02.1x+1T2019/pdfbook/0/chapter/4/16">Chapter 4.5.1 Conductors and Equipotentials</a></li></ul>
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<h2 class="hd hd-2 unit-title">L11v1: Conductors and Insulators</h2>
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Insulators and conductors.
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Consider an object made of metal (a conductor) and the other of plastic (an insulator). They are both charged with a total charge [mathjaxinline]+Q[/mathjaxinline]. The conductor is in electrostatic equilibrium (i.e. the charges are not moving). Which of the following statements are true (check all that apply)? </p>
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<text>1. The electric field inside the insulator is always zero.</text>
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<text>3. The charge can be distributed anywhere inside the volume of the insulator.</text>
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<text>5. The charge is always distributed on the surface of the conductor.</text>
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<text>6. An insulator has no mobile charged particles.</text>
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<text>7. A conductor has mobile charged particles that can move through the material.</text>
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<h2 class="hd hd-2 unit-title">L11v4: Induced Charge on a Conductor from a Charge Inside</h2>
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<h2 class="hd hd-2 unit-title">L11Q2: Point Charge in Conductor 1 and 2</h2>
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Point Charge in Conductor
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<p>
A point charge [mathjaxinline]+Q[/mathjaxinline] is placed inside a neutral, hollow, spherical conductor. As the charge is moved around inside the cavity, the surface charge density on the outer surface </p>
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<img src="/assets/courseware/v1/7e5762a75182dfc2f8b93172c65f883a/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w4_5.svg" width="330"/>
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<text> is initially uniform and does not change when the charge is moved.</text>
</label>
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<text> is initially uniform but does become non-uniform when the charge is moved.</text>
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<text> is initially non-uniform and does not change when the charge is moved.</text>
</label>
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<text> is initially non-uniform but does change when the charge is moved.</text>
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Point Charge in Conductor
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A point charge [mathjaxinline]+Q[/mathjaxinline] is placed inside a neutral, hollow, spherical conductor. As the charge is moved around inside the cavity, the electric field outside the conductor </p>
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<img src="/assets/courseware/v1/7e5762a75182dfc2f8b93172c65f883a/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w4_5.svg" width="330"/>
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<text> is zero and does not change</text>
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<text> is non-zero and does not change</text>
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<text> is zero when the charge [mathjaxinline]+Q[/mathjaxinline] centered but changes</text>
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<text> is non-zero and changes</text>
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<h2 class="hd hd-2 unit-title">L11Q3: Point Charge in Conductor 3</h2>
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Point Charge in Conductor
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A point charge [mathjaxinline]+q[/mathjaxinline] is placed inside the hollow cavity of a conductor that carries a net charge [mathjaxinline]+Q[/mathjaxinline]. What is the total charge on the outer surface of the conductor? </p>
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<text> Zero.</text>
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<h2 class="hd hd-2 unit-title">L11v5: Potential on a Hollow Conductor with a Charge Inside</h2>
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Potential on a Hollow Conductor with a Charge Inside
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<p>
A spherical conductor of radius [mathjaxinline]R[/mathjaxinline] has an asymmetric cavity as shown in the figure. The conductor is uncharged. There is a positive charge [mathjaxinline]q[/mathjaxinline] inside the cavity. </p>
<p><b class="bfseries">(Part a)</b> Calculate the electric potential at any point outside the conductor. Consider the reference of electric potential to be zero at infinity: [mathjaxinline]V(\infty ) = 0[/mathjaxinline]. Express your answer in terms of [mathjaxinline]k[/mathjaxinline], [mathjaxinline]q[/mathjaxinline], [mathjaxinline]R[/mathjaxinline], and [mathjaxinline]r[/mathjaxinline], the distance from the center of the conductor as needed. </p>
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<p style="display:inline">[mathjaxinline]V(r)=[/mathjaxinline] </p>
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<p><b class="bfseries">(Part c)</b> Calculate the electric potential at any point inside the conductor, the gray area (not inside the cavity) the conductor. Consider the reference of electric potential to be zero at infinity: [mathjaxinline]V(\infty ) = 0[/mathjaxinline]. Express your answer in terms of [mathjaxinline]k[/mathjaxinline], [mathjaxinline]q[/mathjaxinline], [mathjaxinline]R[/mathjaxinline], and [mathjaxinline]r[/mathjaxinline], the distance from the center of the conductor as needed. </p>
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<p style="display:inline">[mathjaxinline]V(r)=[/mathjaxinline] </p>
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<h3 class="hd hd-2">L11v05: Potential on a Hollow Conductor with a Charge Inside</h3>
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<h2 class="hd hd-2 unit-title">L11Q4: Connect Two Conductors with Long Wire</h2>
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Metal Spheres Connected by a Wire
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Two conducting spheres with radii [mathjaxinline]r_1[/mathjaxinline] and [mathjaxinline]r_2[/mathjaxinline] are located very far apart (drawing is not to scale) so that the charge distributions on the spheres are uniform. They are connected by a very long thin conducting wire. What is the ratio of the charges [mathjaxinline]q_1/q_2[/mathjaxinline] on the surfaces of the spheres? </p>
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<h2 class="hd hd-2 unit-title">L11v6: Faraday Cage</h2>
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<h3 class="hd hd-2">L11v06: Faraday Cage</h3>
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