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Prove that, if an insulated, uncharged conductor

Question:

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.

Solution:

The electric potential decreasing along the direction of the electric field is given as E = dV/dr

The electric potential decreases when the path from the charged conductor is taken to the uncharged conductor along the direction of the electric field.

This continues when another uncharged conductor is considered to the infinity lowering the potential even further.

This shows that the uncharged body is at intermediate potential and the charged body is at infinity potential.

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