(PI3a(bi-a)+P2(b-a)) E (4xr²) = arrange for E. 3egr?

College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A non-conducting spherical shell of inner radius a1 and outer radius b1 is uniformly charged with charge density p1 inside another non-conducting spherical shell of inner radius a2 and outer radius b2 that is also uniformly charged with charge density p2. Find the electric field at space point P at a distance r from the common center such that (a) r > b2 (b) a2 < r < b2 (c) b1 < r < a2 (d) a1 < r < b1, and (e) r < a1.

 

MY QUESTION:

I just need some clarification on part (a). The problem takes me to the part of E*(4*pi*r2 )= (p1*4/3pi(b1-a1) + p2*4/3pi(b2-a2) as the numerator and then we have epsilon naught. I'm getting caught up on how the denominator ends up being 3*pi*epsilon*r. Can you do a step by step for that, please?

E (4ar²) =
Rearrange for E.
E =
3egr?
Transcribed Image Text:E (4ar²) = Rearrange for E. E = 3egr?
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