Electric field & energy in a spherical distribution of charge

[Cocoleia]

Homework Statement

Homework Equations

Gauss

The Attempt at a Solution

I am really confused with question a, I have an idea of how to answer b and c once I obtain an answer for part a... My best guess would be to use Gauss, but I am not sure. Would the field inside be 0? What will the bounds of integration be when I integrate to find the charge, right now I get a charge of 2pi(a^3)? I am working on my solution and will post a picture when I get something useful, but can someone explain? Thank you.

 

[BvU]

Choose a suitable volume to write out your relevant equation in terms of the variables and post your working...

 

[haruspex]

The question is a bit unclear. I assume that a/r is for the charge density at a distance r from the centre of the sphere radius a.

 

[BvU]

I agree (as almost always ). It is unclear in the sense that (most probably) the composer forgot to mention 'for $r\le a$' in $'\rho = ...' \$; and $\rho = 0\$ for $r>a$ ' so you make that assumption, mention it in your answer, and continue with the exercise.

 

[Cocoleia]

Homework Statement

Homework Equations

The Attempt at a Solution

I am at the first part of the question. For the inside field, I did the following (and the same for the outside, just using different bounds of integration)

In the given solution, they use electric displacement

Why not just use Gauss' law like usual, like I did?

 

[BvU]

They do. $\vec D=\varepsilon \vec E$.

I will ask a mentor to move this to the identical thread you started a week ago ...