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--- 184_notes:examples:week2_charged_thing_neutral_thing [2017/08/25 03:17] – tallpaul
+++ 184_notes:examples:week2_charged_thing_neutral_thing [2018/05/17 15:56] (current) – curdemma
@@ Line 1: / Line 1: @@
+[[184_notes:charge_and_matter|Return to Charge and Matter]]
 ===== Example: Interactions Between Charged and Neutral Objects =====
-Suppose we have a positively charged object near a conductor. What happens to the charge distribution of the conductor when we bring an identical positively charged object near to the other side of the conductor? The situation is pictured to the right.
+Suppose we have a positively charged object near a conductor. What happens to the charge distribution of the conductor when we bring an identical positively charged object near to the other side of the conductor? The situation is pictured below.
-{{ 184_notes:2_charged_neutral_thing_intro.png?300|Charge Distribution Induced From Two Sides, Setup}}
+{{ 184_notes:2_charged_neutral_thing_intro.png?300 |Charge Distribution Induced From Two Sides, Setup}}
 ===Facts===
-  * Electrons in an insulator are tightly bound to the nucleus.
+  * Mobile charges in a conductor can move easily through the material.
-  * Charges cannot move freely through an insulator.
+  * The conductor is neutral (total net charge is $0 \text{ C}$).
+  * A smaller distance between charges means a stronger interaction.
-===Lacking===
+===Goal===
-  * An explanation for whether it is possible to charge a pair of insulators using induction.
+  * What will the charge distribution in the neutral conductor look like?
+/*
 ===Approximations & Assumptions===
-  * We are talking about pure insulators, so we can use the facts listed.
+  * The conductor is initially neutral.
-  * By pure insulators, we mean there are no electrons on the surface that are not bound to any nuclei.
+  * The final charge distribution is not affected by which charged object was nearby first.
-  * By induction, we mean the process shown in the figure to the right.
+  * The setup of the charged objects and the neutral conductor is symmetric.
+  * The objects are not touching the conductor, but are close enough to affect the charge distribution.
 ===Representations===
-  * We can model the atoms in an insulator as little ovals, that show when one side of the atom is more positive or negative than the other side. When ovals are not shown, this will just mean the atoms are not polarized.
+  * In our diagram, we can represent electrons with red subtraction signs, and we can represent the positive nuclei they leave behind with blue addition signs.
-  * We can use a similar diagram as the induction figure in the notes, since we assume it is the same process.
+*/
+====Solution====
+A key fact here is that a **smaller distance between charges means a stronger interaction**. Consider the left-most region of the neutral conductor. The left object attracts negatively charged particles to this region, while the right object repels positively charged particles to this region. It turns out, though, this edge would **not** be neutral Since the left object is closer to this left-most region, its interaction is stronger than the right object, and we end up with a net negative charge in this region. Similarly, the right-most region also has a net negative charge. Since we assumed the conductor is neutral, the positive charge needs to go somewhere, too! The only region remaining is the middle, which must have a net positive charge in order for the conductor to remain neutral. A new representation is shown below. \\
+{{ 184_notes:2_charged_neutral_thing_solution.png?200 |Charge Distribution Induced From Two Sides, Solution}}