Electric Field of a solid sphere of non-uniform surface density

[vtv]

A solid sphere has surface charge density, Rho (r)

Rho(r) = k ₁ ( 0 < r < a)

k₂ x ( a < r < R)

2) Find the electric field in all region i.e 1) r < a and 2) a < r < R and 3 ) R <
The attempted solution and the question with the diagram is attached below

Could the answer be verified particularly for region 2 ?!

<< Mentor Note -- fixing up picture some... >>

 

[Orodruin]

What you describe is not a surface charge density. It is just a charge density.

Even with the mentors cleaning up your image it is difficult to read (and impossible to quote). I suggest that you type it out and explicitly flesh out your argumentation for each step.

 

[haruspex]

k₂ x ( a < r < R)

What does this mean? Should it be just k₂, or perhaps k₂r?