184_notes:examples:week5_flux_two_radii

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184_notes:examples:week5_flux_two_radii [2021/05/29 21:09] – schram45184_notes:examples:week5_flux_two_radii [2021/06/04 00:47] (current) – schram45
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   * $\Phi_e$ for each sphere   * $\Phi_e$ for each sphere
   * $\text{d}\vec{A}$ or $\vec{A}$, if necessary   * $\text{d}\vec{A}$ or $\vec{A}$, if necessary
- 
-===Approximations & Assumptions=== 
-  * There are no other charges that contribute appreciably to the flux calculation. 
-  * There is no background electric field. 
-  * The electric fluxes through the spherical shells are due only to the point charge. 
-  * Perfect spheres. 
-  * Constant charge for the point charge (no charging/discharging). 
  
 ===Representations=== ===Representations===
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   * We represent the situation with the following diagram. Note that the circles are indeed spherical shells, not rings as they appear.   * We represent the situation with the following diagram. Note that the circles are indeed spherical shells, not rings as they appear.
 [{{ 184_notes:5_flux_two_radii.png?300 |Point charge and two spherical shells}}] [{{ 184_notes:5_flux_two_radii.png?300 |Point charge and two spherical shells}}]
 +
 +<WRAP TIP>
 +===Approximations & Assumptions===
 +There are a few approximations and assumptions we should make in order to simplify our model.
 +  * There are no other charges that contribute appreciably to the flux calculation.
 +  * There is no background electric field.
 +  * The electric fluxes through the spherical shells are due only to the point charge.
 +The first three assumptions ensure that there is nothing else contributing or affecting the flux through our spheres in the model.
 +  * Perfect spheres: This will simplify our area vectors and allows us to use geometric equations for spheres in our calculations.
 +  * Constant charge for the point charge: Ensures that the point charge is not charging or discharging with time.
 +</WRAP>
 +
 ====Solution==== ====Solution====
 Before we dive into calculations, let's consider how we can simplify the problem by thinking about the nature of the electric field due to a point charge and of the $\text{d}\vec{A}$ vector for a spherical shell. The magnitude of the electric field will be constant along the surface of a given sphere, since the surface is a constant distance away from the point charge. Further, $\vec{E}$ will always be parallel to $\text{d}\vec{A}$ on these spherical shells, since both are directed along the radial direction from the point charge. See below for a visual. A more in-depth discussion of these symmetries can be found in the notes of [[184_notes:eflux_curved#Making_Use_of_Symmetry|using symmetry]] to simplify our flux calculation. Before we dive into calculations, let's consider how we can simplify the problem by thinking about the nature of the electric field due to a point charge and of the $\text{d}\vec{A}$ vector for a spherical shell. The magnitude of the electric field will be constant along the surface of a given sphere, since the surface is a constant distance away from the point charge. Further, $\vec{E}$ will always be parallel to $\text{d}\vec{A}$ on these spherical shells, since both are directed along the radial direction from the point charge. See below for a visual. A more in-depth discussion of these symmetries can be found in the notes of [[184_notes:eflux_curved#Making_Use_of_Symmetry|using symmetry]] to simplify our flux calculation.
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  • Last modified: 2021/05/29 21:09
  • by schram45