A point charge q is placed at a distance r from centre of a conducting . . .

Question : A point charge q is placed at a distance r from centre of a conducting neutral sphere of radius R (r>R). The potential at any point P inside the sphere at a distance r₁ from point charge due to induced charge of the sphere is given by :  

(1) Kq/r₁ - Kq/R
(2) Kq/r - Kq/R
(3) Kq/r - Kq/r₁
(4) -Kq/r₁ - Kq/R

Doubt by Saatvik

Solution : 

When a point charge q is placed at a distance r (where r>R) from the center of a neutral conducting sphere of radius R, it induces surface charge on the sphere.

Here it must be noted that induced charged are not equally distributed on the surface of the sphere but the sum of net charge must be zero because the sphere is neutral. It is denser near the side facing the external charge and rarer on the surface which is away from the charge. 

Total Potential at Point P = Potential due to real charge + Potential due to induced charge.

Total Potential at point P = Potential at any point inside the sphere (including point O) because potential at any point inside the sphere is constant. 

Total Potential at Point P=Potential at point O 
=kq/r

Potential at point P due to external real charge q = kq/r₁

ATQ

Total Potential at Point P = Potential at point P due to external real charge q + Potential due to induced charges at P

kq/r = kq/r₁ + Potential due to induced charges at P

Potential due to induced charges at P 

= kq/r-kq/r₁

So, (3) Kq/r - Kq/r₁, would be the correct option. 

Similar Question : 

A point charge q is placed at a distance r from centre of an uncharged conducting sphere of radius R (r>R). The potential at any point on the sphere is 

(1) KQ/R

(2) Zero 

(3) KQ/2R

(4) 2KQ/R

Ans : (1) KQ/R