Understanding Ohm's Law: Electric Current & Potential Difference

[donaldparida]

According to Ohm's law, "Physical conditions remaining the same, the electric current flowing through a conductor is directly proportional to the potential difference across the two ends of the conductor"
I have two conceptual queries:
FIRST
When the ends of the conductor are not connected to any external electric potential difference source, the electric potential throughout the conductor remains the same and the electric potential difference across any two arbitrarily selected points in the conductor is 0. Am i correct in saying this?
SECOND
When the ends of the conductor are connected to an external electric potential difference source, the ends of the conductor attain different electric potentials and current exists across the conductor. Every point in the conductor is at different electric potential and the electric potential decreases from one end to the other. Ohm's law can be applied for any two arbitrarily selected points in the conductor in this case and not only for the ends or terminals of the conductor. Am i correct in saying this?
Also does charge require any potential difference to flow across a conductor(ideal)?(V=IR=>V=I*0=>V=0, according to me)

 

[cnh1995]

When the ends of the conductor are not connected to any external electric potential difference source, the electric potential throughout the conductor remains the same and the electric potential difference across any two arbitrarily selected points in the conductor is 0. Am i correct in saying this?

Yes.

When the ends of the conductor are connected to an external electric potential difference source, the ends of the conductor attain different electric potentials and current exists across the conductor. Every point in the conductor is at different electric potential and the electric potential decreases from one end to the other. Ohm's law can be applied for any two arbitrarily selected points in the conductor in this case and not only for the ends or terminals of the conductor. Am i correct in saying this?

Ideally no, practically yes.

Ideal conductors have zero resistance. If you connect the terminals of an ideal voltage source (zero internal resistance) with an ideal conductor, you'll have infinite current. So this is not a valid situation in circuit theory.

Practically, every conductor has a non-zero but very small resistance and hence, there is a small voltage drop across the conductor. This voltage drop, being negligibly small, is often neglected in practice and the conductors are assumed to be ideal.