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Conductors have unique properties when it comes to their behavior in electrostatics. One of the key traits is that the electric potential throughout a conductor in electrostatic equilibrium is uniform. This means that no matter where you measure the potential inside the conductor, it will be the same.
In electrostatics, the electric field inside a conductor is zero. This occurs because any external electric fields cause charges within the conductor to move until they reach a state of equilibrium. These moved charges will cancel out the internal electric fields, resulting in zero net electric field inside the conductor.

• Zero electric field means zero force acting on free charges inside.
• Hence, they do not move, confirming equilibrium.
• The potential throughout remains the same because potential difference is caused by electric fields, which are absent inside.

This characteristic of conductors under electrostatic conditions ensures that the potential is uniform and the entire conductor behaves like a single equipotential surface.

A hollow metal sphere is a specific type of conductor. Its hollow interior doesn't affect its external properties when charged. Being a perfect conductor, a charged hollow metal sphere displays uniform potential across both the outer surface and the inner cavity.
Due to its conducting nature:

• The charges distribute themselves evenly on the outer surface.
• The electric potential is equal throughout the sphere — so the potential inside the cavity, including its center, matches the potential on the outer surface.

The hollow part of the sphere means its inside is devoid of any charges. Yet the principles of electrostatics ensure that regardless of the presence of charge internally, the entire conductor surface remains at an equal potential.
In the example provided, the sphere's potential at its surface, as well as anywhere inside, is given as 10 V. Regardless of where you are within the sphere — at the center or near the walls — the potential stays constant.

Inside a conductor at electrostatic equilibrium, the electric field is not simply small; it is zero. This is a significant behavior that determines several neat properties of charged conductors. With no electric field inside, there is no force acting on any charge carriers, and thus no movement of charges occurs within the conductor.
This absence of an internal electric field ensures that any charge resides entirely on the surface of the conductor. This applies equally to charged hollow spheres:

• Outside the sphere, the electric field behaves as it would for a point charge at the center — decreasing with distance from the surface.
• Inside, the sphere acts like an electrostatics safe zone — no net electric field and no varying electric potential.

Understanding this aspect is crucial, as it underlies the fact that the electric potential inside a hollow metal sphere is uniform and matches the potential at the surface. Thus, if the surface is at 10 V, then throughout — including the center — the potential remains 10 V.