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pinnaka

After A request made by Indian army to solve this Question. But I found that the Question was not stated properly
But Now I have a got a copy of iit paper the Question is

Q) A sphericsl portion has been removed from a solid sphere having charge uniformly disturburted through out the volume. The E inside the emptied space is -----

The ans is it is uniform and non zero

NO it is given in the Q that the charge is distributed uniformly throughout the entire volume therfore the sphere is not a conducting sphere. If it were to be the enitre charge ould reside on the surface

Here is the mathematical proof
The E of a solid sphere of uniform density is Qr/4*pie*R^3
E = rho*r/3eplison_0
E(vector) = rho*r(vector)/ 3*eplison_0-----
Now assume that the removed portion is a disatnce b (center of cavity) from the center of the sphere
A point inside the sphere is located by r-b (vector from)

---Hope taht helps
E = E(uniform) +E(hole)
E unifrom represents the sphere of uniform charge rho and E(hole) of charge density -rho
inside the cavity net charge is zero
E(uniform) = rho*r/3*eplison_0
E_hole = - rho*(r-b) {vector form)/3*eplison_0
then E = pb(vect0r)/3*eplison_0
Therfore this magnitude is consant and non zero

therefore the ans non zero and constant electric filed

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