Question

Two sphere A and B of radii 17 cm each and having charges of 1 and 2 coulombs respectively are separated by a distance of 80 cm. The electric field at a point on the line joining the centres of two spheres is approximately zero at some distance from the sphere A. The electric potential at this point is

Answer 1

Let the point be P at a distance of  x cm from A.  We assume P is outside the spheres A and B , between them.

    Since the distance between them is much larger than radii, they can be treated as point charges for the purpose of Electric field and potential at P.

E at P = K * 1/x^2 - K * 2/(0.80-x)^2 = 0
                 2 x^2 = 0.64 +x^2 - 1.60 x 
                    x^2 +1.60 x - 0.64 = 0
                    x1 = + 80 (√2 - 1)  cm       or  x2 = - 80(√2+1) cm
                           = 33.14 cm                               = - 193.1 cm
so there are two points at which field is 0.

The point P1 (x1 from A) is in between spheres.   The point P2 (at x2) is outside on the line between two spheres. 

For point P1:   V = 9*10^9 [1/0.3314 + 2/0.4686]  Volts

for point P2  =  V = 9*10^9 [1/1.931 +   2/2.731 ]  volts