E & M: Charges, Gauss & Volts

VERSION # 2.10

Last Updated 6:38 PM 2/20/2019

Take a look at each of these... how long does it take you identify which is which?

`k_e (q_1q_2)/r^2`
`k_e q_1/r^2`
`k_e (q_i)/r_i`
`k_e (q_1q_2)/r`
`k_e(dq)/r`
∫`(dV)/dx`
   

Here's an interesting thought for you:

Lets say we have a sphere made of some insulating material (electrons are NOT free to roam) with uniform charge distribution and we're trying to find the electric field at some point inside the sphere and at another point outside the sphere.

What role (if any) does the the fact that the sphere is an insulator play in your investigations?

What role (if any) does the fact that the sphere has uniform charge density play in your investigations?

How (or should?) you use Gauss's Law in each case?

Here's ANOTHER interesting thought for you:

Lets say we have a sphere made of some conducting material (electrons are most definitely free to roam) and we're trying to find the electric field at some point inside the sphere and at another point outside the sphere.

What role (if any) does the the fact that the sphere is an conductor play in your investigations?

Why can we infer that the the sphere has a uniform charge density? Why do we like that?

How (or should?) you use Gauss's Law in each case?

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  • You MAY find this document (courtesy of the University of Utah physics dept) rather helpful
  • This article from the University of Salford in the UK provides helpful things Gauss too!
  • Our friends at Georgia State University (Hyperphysics.com) have THIS to say...

Please do the following problems. As always, make a solid effort at the problem before looking at my solutions (sorry about the images I had to use my phone)

Problem 24.29 is fairly basic Gauss:

Try problem 24.35 on page 742 is kinda interesting (generally). Please annotate your work to help you zero-in on what you understand and what might be a bit scattered at this point.

Probelm 24.36 helps with the whole insulating thingy...

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