why repulsion is the sure test to find whether a object is charged or not.
Repulsion is said to be the sure test to find whether an object is charged or not because attraction can occur between an uncharged body and a charged body due to induction of charges from the charged body to the uncharged body. But repulsion can take place only between two charged bodies.
When a charged body is brought near an uncharged body, the charged body will induce an opposite charge on the uncharged body. This will lead to attraction between the two bodies, which might give a false impression that the uncharged body possesses some charge.
Although for repulsion, both bodies need to carry same kind of charge which is possible only if they themselves are charged (cannot be done via induction). Hence repulsion is the sure test to find whether an object is charged or not.
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