I finally managed to calculate the V(r) for all r by using the E(r) for all r that I had calculated. It would be great if someone could take a look at it to see if it is correct. Thank you.
Page 1: http://i.imgur.com/fKsv7j4.jpg
Page 2: http://i.imgur.com/uCL7amL.jpg
Page 3...
Ahhhh. I understand now. I see my mistake. I have recalculated with the proper dielectric constants now I hope. Is my E(r) for all r correct now ?
http://i.imgur.com/bI87guV.jpg
As stated by Tanya, I take the algebraic sum of the two charges i.e ρ1V1+ρ2V2 when integrating to find E. Thus for r > c, I have ρ1V1 and p2V2 in the equation which leads to me having ε1 and ε2 in the final equation for E for r > c. This equation is what I use when integrating for V.
Here is...
I have calculated the V(r) for all r by using the E(r) for all r that I had calculated. I am not sure if it is completely correct. It would be great if someone could take a look at it to see if it is correct. I know it is a lot of pages but it would be help me a lot to know if I have solved this...
Hey,
I have now done this correction that you pointed out. I can't believe it was quite this easy (if i have understood what you meant correctly). I have linked my solution for E(r) for all r now. Is it correct?
Page 1: http://i.imgur.com/hiEvBPw.jpg
Page 2: http://i.imgur.com/0mdblxs.jpg...
Hello Tanya,
These two parts you mentioned are the ones that I am not sure how to calculate. I do not know how to add the charge for region a<r<b for Page 2 and b<r<c for Page 3. Do I just multiply it in ? How do I proceed here?
Homework Statement
Three volumes bounded by three concentric spheres with radii a, b and c. The innermost volume r<a, consists of vacuum. Next volume, a<r<b, is filled with a material having a constant volume charge density ρ1 and a relative dielectric constant ε1. The external volume...
Ok, I will do this change and rewrite my answer. It would be great if you could take another look then and let me know if it is correct. Thanks again for all your help.
That was the sign I was not sure about. I had written r = ay. Should it not be r = a(-y) because it points in the negative Y direction hence the negative sign?
This should mean that the fields of the two straight line segments do not cancel each other because they point in the same direction...
Hey TSny,
Does this mean my BL1 is incorrect which leads to the fact that my total magnetic field B is incorrect? Can you specify what mistake you have found? When I calculated BL1 I was unsure about the signs of r and r'.