HELP!
An insulating spherical shell of inner radius R1 and outer radius R2 has a charge density
$$ρ = ρ0r{2}/R^{2}-{1}$$
a: Determine the electric field everywhere in space and graph |E~ | versus r.
b: You have a conductor of radius R2. What surface charge density is needed for it to
produce the same electric field for r R2 as the insulating sphere does?

Question

HELP! 
An insulating spherical shell of inner radius R1 and outer radius R2 has a charge density
$$ρ = ρ0r{2}/R^{2}-{1}$$
a: Determine the electric field everywhere in space and graph |E~ | versus r.
b: You have a conductor of radius R2. What surface charge density is needed for it to
produce the same electric field for r > R2 as the insulating sphere does?

kkutie7 · Answer

|dw:1454207240154:dw|

kkutie7 · Answer

@satellite73

michele_laino · Answer

hint:
since we have an electrostatic field, then we can apply this equation of Maxwell:
$$\huge {\text{div}}{\mathbf{E}} = 4\pi \rho \left( r \right)\quad \left( {CGS} \right)$$

please use the spherical polar coordinates, in order to make the needed computations

kkutie7 · Answer

Never seen the equation before. I just thought that we have to go layer by layer. I was going to start with $$E_{r>R_{2}}$$
and I read somewhere that it is like a point charge?
That's as far as my understanding goes.

anonymous · Answer

Just ask for assistance here - submit your instructions to experts https://assignment.essayshark.com/blog/looking-for-physics-assignment-help/

michele_laino · Answer

What I wrote is a differential form of the Maxwell equation. Maybe you have seen such equation in integral form, namely:
$$\huge  \Phi \left( {\mathbf{E}} \right) = 4\pi {Q_{enclosed}}$$
I have used the CGS system.
Namely the flux of the electric field through a closed surface, is proportional to the electric charge inside or enclosed by such closed surface
Please tag me and I will show the solution of your question, since I can not give direct answers
@Kkutie7

irishboy123 · Answer

this is all you need to know https://www.youtube.com/watch?v=QNIJC1emss8 http://www.maxwells-equations.com/gauss/law.php tag me if you need some more help

irishboy123 · Answer

oh, and the total amount of charge in the hollow sphere can be gotten from a spherical integral: http://www.wolframalpha.com/input/?i=%5Cint_%7Bt+%3D+0%7D%5E%7B2+pi%7D+%5Cint_%7Bp+%3D+0%7D%5E%7B+pi%7D+%5Cint_%7Br+%3D+R_1%7D%5E%7BR_2%7D+(rho_o+%2F+R_1%5E2)+r%5E2+r%5E2+sin(p)+dr+dp+dt you will need make the upper limit a variable to get E inside the sphere. |dw:1454368477585:dw|