A Conceptual Difficulty regarding Potentials

[Avi1995]

Plz help me out with this difficulty. Here is a figure showing two conducting spheres(haven't drawn all EF lines):-

Here is the problem, Suppose one of the spheres is charged with a charge +Q, other is neutral
, so charges will get induced as shown in figure. The left portion of orange sphere(neutral one)
is at lower potential than the right portion because it has -ve charge and other is +ve.
Since E=0 inside a conductor, we have:-
dV=-E.dr
so if we move from the point A(on left surface) to B, since E=0 we have,
dV=0
so V_A =V_B
Now if we move from the point C(on right surface) to B, since E=0 we have,
dV=0
so V_B =V_C
but V_a<V_c??
What is wrong in this reasoning?

Homework Equations

dV=-E.dr

 

[SammyS]

Plz help me out with this difficulty. Here is a figure showing two conducting spheres(haven't drawn all EF lines):-

Here is the problem, Suppose one of the spheres is charged with a charge +Q, other is neutral
, so charges will get induced as shown in figure. The left portion of orange sphere(neutral one)
is at lower potential than the right portion because it has -ve charge and other is +ve.
Since E=0 inside a conductor, we have:-
dV=-E.dr
so if we move from the point A(on left surface) to B, since E=0 we have,
dV=0
so V_A =V_B
Now if we move from the point C(on right surface) to B, since E=0 we have,
dV=0
so V_B =V_C
but V_a<V_c??
What is wrong in this reasoning?

Homework Equations

dV=-E.dr

The conclusion in sentence I put in RED above is wrong.