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--- 184_notes:examples:week14_b_field_capacitor [2017/11/27 03:12] – tallpaul
+++ 184_notes:examples:week14_b_field_capacitor [2017/11/28 02:12] – dmcpadden
@@ Line 1: / Line 1: @@
 ===== Magnetic Field from a Charging Capacitor =====
-Suppose you have a parallel plate capacitor that is charging with a current $I=3 \text{ A}$. The plates are circular, with radius $R=10 \text{ m}$ and a distance $d=1 \text{ cm}$. What is the magnetic field in the plane parallel to but in between the plates?
+Suppose you have a parallel plate capacitor that is charging with a current $I=3 \text{ A}$. The plates are circular, with radius $R=10 \text{ m}$ and a distance $d=1 \text{ cm}$ apart. What is the magnetic field in the plane parallel to but in between the plates?
 {{ 184_notes:14_capacitor_picture.png?400 |Charging Capacitors}}
@@ Line 15: / Line 15: @@
 ===Approximations & Assumptions===
   * We are only concerned about a snapshot in time, so the current is $I$, even though this may change at a later time as the capacitor charges.
-  * The electric field between the plates is the same as the electric field between infinite plates.
+  * The electric field between the plates is the same as the electric field between infinite plates (we'll ignore the electric field at the edges of the capacitor).
   * The electric field outside the plates is zero.
@@ Line 26: / Line 26: @@
 {{ 184_notes:14_capacitor_side_view.png?300 |Plane in which we wish to find B-field}}
 ====Solution====
-We wish to find the magnetic field in the plane we've shown in the representations. Due to the circular symmetry of the problem, we choose a circular loop in which to situate our integral $\int \vec{B}\bullet\text{d}\vec{l}$. We also choose for the loop to be the perimeter of a flat surface, so that the entire thing lies in the plane of interest, and there is no enclosed current (so $I_{enc} = 0$). We show the drawn loop below, split into two cases on the radius of the loop.
+We wish to find the magnetic field in the plane we've shown in the representations. We know from the notes that a changing electric field should create a curly magnetic field. Since the capacitor plates are charging, the electric field between the two plates will be increasing and thus create a curly magnetic field. We will think about two cases: one that looks at the magnetic field inside the capacitor and one that looks at the magnetic field outside the capacitor.
+Due to the circular symmetry of the problem, we choose a circular loop in which to situate our integral $\int \vec{B}\bullet\text{d}\vec{l}$. We also choose for the loop to be the perimeter of a flat surface, so that the entire thing lies in the plane of interest, and there is no enclosed current (so $I_{enc} = 0$ - there is only the changing electric field). We show the drawn loop below, split into two cases on the radius of the loop.
 {{ 184_notes:14_capacitor_loops.png?600 |Circular Loops}}
-Below, we also draw the direction of the magnetic field along the loops. We know the magnetic field is directed along our circular loop -- if it pointed in or out a little bit, we may be able to conceive of the closed surface with magnetic flux through it, which would imply the existence of a magnetic monopole. This cannot be the case! We also know that the field is directed counterclockwise, due to the increasing electric field into the page. This comes from an extension of Lenz's Law, upon which discussion is not needed for this course.
+Below, we also draw the direction of the magnetic field along the loops. We know the magnetic field is directed along our circular loop (since the changing electric flux creates a curly magnetic field) -- if it pointed in or out a little bit, we may be able to conceive of the closed surface with magnetic flux through it, which would imply the existence of a magnetic monopole. This cannot be the case! We also know that the field is directed counterclockwise, due to the increasing electric field into the page. (This comes from an extension of Lenz's Law, but will not needed for this course).
 {{ 184_notes:14_capacitor_b_field_loops.png?600 |Circular Loops, with B-field shown}}