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A solid spherical conductor has a conical hole made at one end, ending in a point B , and a small conical projection of the same shape and size at the opposite side, ending in a point A. A cross-section through the centre of the conductor is shown in the figure on the right. If, now, a positive charge Q is transferred to the sphere, then where would the charge density be more?enter image description here

My reasoning is as follows. Since B is closer to most of the points in(and possibly on) the sphere, if more charges accumulate there then there will be more coulumb repulsion and thus the self energy would be more which is why charge density should be more at A and less at B to even things out. Is it correct? If not the please let me know the right reasoning

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You're absolutely right. The charge density at $A$ is indeed higher than the one at $B$, you already gave the reasoning. Further information is given here and here(Chapter "Electric Fields and Surface Curvature")

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