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.

(N/A) The electric field $E = -\frac{dV}{dr}$ indicates that the electric potential $V$ decreases in the direction of the electric field.
Consider a path starting from the charged conductor and moving towards the uncharged conductor along the direction of the electric field lines. Since the field originates from the charged body,the potential $V$ must decrease along this path. Thus,the potential of the uncharged body $V_u$ is less than the potential of the charged body $V_c$ (assuming $V_c > 0$).
Next,consider a path from the uncharged conductor extending towards infinity. Since the electric field lines continue to point away from the charged system towards infinity,the potential must continue to decrease along this path. By definition,the potential at infinity is $V_{\infty} = 0$.
Therefore,the potential of the uncharged body $V_u$ satisfies the condition $V_{\infty} < V_u < V_c$. This confirms that the uncharged body is intermediate in potential between the charged body and infinity.