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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.

 

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The electric potential will decrease in the direction of the electric field. The potential

E=\frac{dV}{dr}

The electric potential will also decrease again when the path from the charged conductor is taken to the uncharged conductor in the direction of the electric field.

This process will continue when another uncharged conductor is considered to the infinity lowering the potential even further.

As a result, the uncharged body is at intermediate potential and the charged body is at infinity potential.

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