Two spherical shells have a common center. A -1.50 x10-6 C charge is spread unif

Question

Two spherical shells have a common center. A -1.50 x10-6 C charge is spread uniformly over the inner shell, which has a radius of 0.050 m. A +5.00 x10-6 C charge is spread uniformly over the outer shell, which has a radius of 0.15 m. Find the magnitude and direction of the electric field at a distance (measured from the common center) of
(a) 0.20 m,
(b) 0.10 m,
(c) 0.025 m.
How do i get the answers below???
(a) E = 7.87E5 N/C radially outward
(b)E = 1.35E6 N/C radially inward
(c) E = 0 N/C no direction

Explanation / Answer

Gauss's Law. E times the area of a sphere is equal to the enclosed charge times a constant.

4r2E = Part c is easiest, that point is inside the inner shell so a sphere drawn there encloses no charge. The E field is zero.

Part a the point is outside, the sphere encloses (5 - 1.5) * 10-6 = 3.5 * 10-6 C. If you calculate q/e0 for that much charge and divide it by the area of a sphere radius 0.20 m you should get your answer.

Part b the point is in between, so disregard the outer shell, a sphere drawn there encloses only the inner charge, do the same calculation with r = 0.15 m

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