Calculating Electric Field Intensity with Two Spherical Shells

[john88]

Hi

Two spherical shells where the inner has a radius a and the outer a radius of b. The inner has a total charge of -Q whereas the outer shell has a total charge +Q. The question is to calculate the electric field intensity everywhere in space.
My question is now, how do I choose the limits for example $$a \leq R \leq b$$ I have two examples below

No point charge in the middle

$$E = 0, 0 \leq R \prec a$$ (not equal to a)

$$E = -\frac{Q}{4\pi\epsilon_{o}R^3} \bold{R}$$ $$a \leq R \leq b$$

$$E = 0, b \prec R \prec \infty$$

A point charge in the middle

$$E = \frac{Q}{4\pi\epsilon_{o}R^3} \bold{R}$$ $$0 \prec R \leq a$$ why set equal to a here and not when there aint no point charge in the middle?

$$E = 0$$ $$a \prec R \prec b$$

$$E = \frac{Q}{4\pi\epsilon_{o}R^3} \bold{R}$$ $$b \leq R \prec \infty$$

 

[Gear300]

A point within a spherical shell experiences 0N/C. For R between a and b, inner shell is effective and outer shell's net effect is 0N/C...this works for even insulators so long as charge is evenly distributed across the shell (question didn't specify whether it was a conductor or something else). If the thickness of the shells is negligible, then you could consider the effect of the inner shell as that due to a point charge.