use the concept of negative mass :
we get the answer as d/3ε (R/2)
Q) There is a uniform solid sphere with charge density 'd' and radius 'R'. Now some part of the solid sphere is removed from it. The removed portion is also a sphere of radius 'R/2'.
Thus we are left with a solid sphere and a spherical cavity inside it. Can you find the electric field distribution inside the cavity.
Given that the distance between the center of the sphere and center of the cavity is 'R/2'.
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i would like to add a question-
a uniform cylindrical wire has a straight cylindrical vent through the wire with its axis at a distance c from the axis of the cylinder.
The radius of the cylinder and vent are R1 and R2 respectively.The given cylindrical wire carries a uniform current i ....find magnetic field at any point inside the vent....
actually the main thing is that the distance between the centers is all that matters in these cases !