Electric field inside and around a hollow sphere

[daanisdenaam]

Hi everyone,

I am wondering if anybody could help me out. For my study I got the following question but I got stuck in part C (see image below).
I Found at A that due to symmetry all components which are not in Ar direction will get canceled out
I found at B that there is only charge density at A<R<B and that it is equal to Pv in that point.

Then I got to part C:
We could fill in the Pv I found at part B, but that will still leave us with the fact that we have to invert the divergent. How could I do that? Does anyone have suggestions on this? That would really help me out!

https://photos-1.dropbox.com/t/2/AAA5802MNhxctUNcDK90azmM498HJ3gjxg7YrJCsRUX69w/12/68628516/jpeg/32x32/1/1444140000/0/2/Question.JPG/CKTg3CAgASACIAMgBiAHKAEoAigH/e1NKusj17g3cy1mlk21YV6Hw7Het1Ozyl9GsFbSYOcg?size_mode=5

 

[BvU]

Hello Daan, welcome to PF !

Nice exercise. Usually you get to work it out this one with Gauss in integrated form (which you can still do, of course).
What do you make from the given hint ? It is the divergence written out in spherical coordinates, a 2^nd order differential equation in r.
To be solved for three regions, each with two conditions.

 

[daanisdenaam]

Hello Daan, welcome to PF !

Nice exercise. Usually you get to work it out this one with Gauss in integrated form (which you can still do, of course).
What do you make from the given hint ? It is the divergence written out in spherical coordinates, a 2^nd order differential equation in r.
To be solved for three regions, each with two conditions.

Thank you a lot for your answer! I Had a look at the given hint indeed, and when I looked again today it helped me out. I solved is as follows:
https://photos-4.dropbox.com/t/2/AADNoUHAGfzLPhMdD5iqnRxngz8zujp0NsI8nrRadbLCIA/12/68628516/jpeg/32x32/1/_/1/2/20151007_144945.jpg/EIrlrDUY89IBIAEoAQ/plpDHjcfvOORwGnKrg3tM1k8Rdy6xOOO5ERIbDhRr30?size=1280x960&size_mode=2