Σ free on two dielectric spherical surfaces

[guyvsdcsniper]

Homework Statement

σ 1 and σ 2 are pasted to 2 spherical dielectric surfaces w/ radius r and 2R

2.)Calc. E when r<R and r>2R
3.)Calc E when R<r<2R

Relevant Equations

Dipole Potential

I have found the total dipole moment of for this problem but am having trouble finding the electric field.

I believe my electric field when r>2R ( I mistakenly wrote it as r<2R on my work, but it is the E with a coefficient of 2/3) is correct as it fits the equation:

.
I don't believe this formula applies inside the sphere though, just based off experience with other problems because with other problems, I don't get that 2cosθ +sinθ. Which is making me second guess my E for r<R. Mathematically it seems correct but I feel I may be missing something fundamental.

Do my E.F. for r<R and r>2R seem correct?

 

[kuruman]

Please show the complete statement of the problem as given to you. Specifically, do you have analytic expressions for $\sigma_1$ and $\sigma_2$? The figure shows σ1=4σcosθ on the inner sphere which I can interpret as $\sigma_1=4\sigma \cos\!\theta$ but then I see on the outer sphere σ2=σdos0 which I don't know how to interpret and which reminds of covfefe.

 

[berkeman]

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