Potential Inside a Conductor

The potential inside a conductor that is carrying charge is an interesting concept in electrostatics. To understand why the correct answer is option 'D' (remains same throughout the conductor), let's break down the explanation into different sections.

1. Potential and Electric Field:
- The potential at a point in an electric field is defined as the amount of work done to bring a unit positive charge from infinity to that point.
- The electric field inside a conductor is zero because charges in a conductor quickly redistribute themselves to cancel any external electric field.
- Since the electric field is zero, no work is done in bringing a charge from one point to another inside the conductor. Therefore, the potential remains the same throughout the conductor.

2. Conductors and Electrostatic Equilibrium:
- Conductors are materials that allow the easy flow of charges.
- In electrostatic equilibrium, the charges inside a conductor are at rest and do not experience any net force.
- Any excess charge placed on a conductor spreads uniformly on its surface, creating an electric field inside the conductor of zero magnitude.
- This redistribution of charges continues until the electric field inside the conductor is zero, ensuring the conductor is in electrostatic equilibrium.

3. Gauss's Law:
- Gauss's law states that the electric field at any point inside a conductor is zero.
- If there were a variation in potential inside the conductor, an electric field would exist, contradicting Gauss's law.
- Therefore, the potential inside a conductor must remain the same throughout.

Conclusion:
Based on the explanations above, we can conclude that the potential inside a conductor remains the same throughout, regardless of whether the charge is given to the conductor. This is due to the fact that the electric field inside a conductor is zero, and charges redistribute themselves until they reach an electrostatic equilibrium.