- #1

Sudharshan

- 22

- 0

## 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, b<r<c, consists of a different material with ρ2 respective ε2. Outside the spheres, r> c, in vacuum.

Find E(r), V(r) for all r.

I.e. r<a, a<r<b, b<r<c, r>c

## Homework Equations

Guass's Law, http://en.wikipedia.org/wiki/Gauss%27s_law

Electric Potential, http://en.wikipedia.org/wiki/Electric_potential

## The Attempt at a Solution

I have calculated the E(r) and V(r) for all r. However, I am not sure about certain E(r), especially E(r) for b<r<c and r>c which leads to my total E(r) and the calculations of V(r) of possibly being wrong. I am also not certain about certain V(r), especially V(r) for b<=r<=c and r<=a. Is my solution correct? Is E(r) and V(r) for all r correct?

Page 1: http://i.imgur.com/XckQoCM.jpg Equations used for calculation of E(r), Calculation of E(r)

Page 2: http://i.imgur.com/5ldfQHL.jpg Calculation of E(r)

Page 3: http://i.imgur.com/bn7ui8S.jpg Calculation of E(r), Total E(r) for all r.

Page 4: http://i.imgur.com/1SxJAP6.jpg Equation used for calculation of V(r), Calculation of V(r)

Page 5: http://i.imgur.com/RRCKCOb.jpg Calculation of V(r)

Page 6: http://i.imgur.com/Ihud14e.jpg Calculation of V(r), Final V(r).

Any help is appreciated.