Gauss's Law: When to Use r & R in Charged Spheres

[vladittude0583]

This question is regarding the application of Gauss's Law to find the electric field within given objects, etc. For example, the question asks you to find the electric field inside a charged sphere, but how do you know when to use little "r" and big "R" when it comes to the radius?

Here are two problems that I just did and got the wrong answer because I had used the incorrect "r."

Problem 1:
Use Gauss's Law to find the electric field inside a uniformly charged sphere (charge density rho)

Problem 2:
Find the electric field inside a sphere which carries a charge density proportional to the distance from the origin, rho = kr, for some constant k. (Hint: This charge is not uniform, and you must integrate to get the enclosed charge).

My question is on problem 1, they used little "r" to denote the radial distance to the Gaussian spherical surface within the sphere and used big "R" to denote the radial distance from the origin (center of sphere) to the outer surface of the sphere. However, on problem 2, they only used little "r" to denote the radial distance to from the origin to the surface of the Gaussian surface. In both scenarios, the Gaussian sphere is contained within the charged sphere. Thus, how do you determine when one "r" value is relevant or if you need both big and little r?

Thanks.

 

[D H]

I don't know how to put this delicately, so I'll just be blunt. You need to read the problem statement carefully. There are only so many letters in the alphabet. The variable x might well have different meanings in problems (just picking a couple of numbers at random) 5 and 8.

In this case, do the first problem first. Don't worry about the second problem until you have the first one answered. The answer to that problem will tell you why the second problem doesn't have a big R in it.

 

[chrisk]

Show how you attempted to solve the problems so the errors can be addressed.

 

[AEM]

I'll add a little bit to D H's response. The letters "r" and "R" have meaning only in the context of the problem posed and the sketch you make to go with it. Understanding the "bits and pieces" of the problem is how you know which letter to use in a given situation. After you read a problem through, go back and pick it apart phrase by phrase to understand what you're given and what you have to work with.