184_notes:examples:week5_gauss_ball

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision		 Previous revision
Last revisionBoth sides next revision
184_notes:examples:week5_gauss_ball [2021/06/07 13:51] – schram45184_notes:examples:week5_gauss_ball [2021/06/07 14:00] – [Solution (Part A)] schram45
Line 12: Line 12:
   * The "Gaussian surface" we will use for our application of Gauss' Law.   * The "Gaussian surface" we will use for our application of Gauss' Law.
   * $\vec{E}(\vec{r})$   * $\vec{E}(\vec{r})$
- 
-===Approximations & Assumptions=== 
-  * The ball is a perfect sphere. 
-  * There are no other charges that affect our calculations. 
-  * The ball is not discharging. 
-  * The ball is uniformly charged throughout its volume. 
-  * For the sake of representation, we assume $Q>0$ (we don't make this assumption for the calculation, it just helps to visualize little charges as little $+$ signs). 
  
 ===Representations=== ===Representations===
Line 27: Line 20:
   * We represent the situation with the following diagram. The insulating case (part A) is shown on the left, and the conductor (part B) is on the right.   * We represent the situation with the following diagram. The insulating case (part A) is shown on the left, and the conductor (part B) is on the right.
 [{{ 184_notes:5_ball_insulator_conductor.png?400 |Charged Ball as an Insulator or Conductor}}] [{{ 184_notes:5_ball_insulator_conductor.png?400 |Charged Ball as an Insulator or Conductor}}]
 +
 +<WRAP TIP>
 +===Assumptions===
 +There are a few assumptions that can be made to simplify down our model before starting any calculations.
 +  * There are no other charges that affect our calculations.
 +  * The ball is not discharging.
 +  * For the sake of representation, we assume $Q>0$ (we don't make this assumption for the calculation, it just helps to visualize little charges as little $+$ signs).
 +</WRAP>
 +
 ====Solution (Part A)==== ====Solution (Part A)====
 A step-by-step approach to using Gauss' Law is shown in the [[184_notes:gauss_ex|notes]] for a line of charge. We will take a similar approach here. A step-by-step approach to using Gauss' Law is shown in the [[184_notes:gauss_ex|notes]] for a line of charge. We will take a similar approach here.
Line 46: Line 48:
 <WRAP TIP> <WRAP TIP>
 ===Approximation=== ===Approximation===
-In order to take the electric field term out of the integral we must assume our ball is a perfect sphere. Having a perfect sphere ensures all the area vectors are parallel to the electric field vectors. This also ensures that the electric field is constant through our Gaussian surface at a given radius.+In order to take the electric field term out of the integral we must approximate our ball as a perfect sphere. Having a perfect sphere ensures all the area vectors are parallel to the electric field vectors. This also ensures that the electric field is constant through our Gaussian surface at a given radius.
 </WRAP> </WRAP>
  
Line 77: Line 79:
          \end{cases}          \end{cases}
 \] \]
-Outside the ball, the electric field exists as if the ball were a point charge!+Outside the ball, the electric field exists as if the ball were a point charge! 
 ====Solution (Part B)==== ====Solution (Part B)====
 We repeat the process above for the case that the ball is a conductor. Notice that much of the reasoning is the exact same. We still have spherical symmetry, and we choose the same Gaussian surface. It is pictured below for both $r<R$ and $r>R$. We repeat the process above for the case that the ball is a conductor. Notice that much of the reasoning is the exact same. We still have spherical symmetry, and we choose the same Gaussian surface. It is pictured below for both $r<R$ and $r>R$.
  • 184_notes/examples/week5_gauss_ball.txt
  • Last modified: 2021/06/07 14:02
  • by schram45