Prove that, if an insulated, uncharged conductor is placed near a charged conductor and no other conductors are present, the uncharged body must be intermediate in potential between that of the charged body and that of infinity.

Explanation

In the given question an uncharged conductor is placed in front of a charged conductors. We have to prove that the electric potential of the uncharged conductor placed in front of the charged conductor is intermediate between that of the charged object and the infinity. The uncharged conductor will get some induced charge and electric field of charged conductor will continue till infinity as shown in figure. The magnitude of the electric field intensity is related with the electric potential as:
`E= -(dV)/(dr)`
Thus, the electric potential difference between any two points, say A and B in the electric field is given by:
`intdV= -int_(A)^(B) vecE. d vecr`
`V_(A)-V_(B)=-int_(A)^(B)vecE. d vecr`
Potential decreases along the direction of electric field and becomes zero at infinity. Hence, potential at the location of uncharged conductor will be intermediate to potential of the charged body and infinity. Moreover, it remains constant within the thickness of conductor.