Q. When a positively charged, conductor is placed near an earth connected conductor, its potential

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Solution:

When a charged conductor is placed near the grounding system, due to induction of charge on the grounded conductor, there is always a drop in the potential.
Because of the connection of conductor with the ground, its potential must be zero but when a charged conductor is placed near it then due to induction of charge replacement occurs inside the grounded conductor.
Hence, a potential difference is created inside of it but it's potential must be equal to zero always because it is grounded.
A fall in potential occurs to equalize the potential up to ground because its potential always will be dropped.