A solid insulating sphere of radius 5 cm carries electric charge uniformly distributed throughout its volume. Concentric with the sphere is a conducting spherical shell with no net charge as shown in Figure OQ24.9. The inner radius of the shell is 10 cm, and the outer radius is 15 cm. No other charges are nearby. (a) Rank the electric flux through concentric spherical surfaces through points A, B, C, and D. Display any cases of equality in your ranking.
1.A > B > D > C
2.B = D > A > C
3.D > B = D > A
4.C > B > A = D
5.None of these
Question 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