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After solving a few questions i have observed two things...Are they true?:

When two identical metallic spheres, one uncharged and one charged with lets say +4Q are brought close to each other then the charges are shared like +2Q and +2Q in both..True?..If true why? Also i have noticed that when the shells are non identical, i.e.suppose a small metal sphere with charge +Q is placed at the centre of a large uncharged spherical shell..then opposite and equal charges are transferred from the smaller inner sphere to the inner part of the large sphere....True?

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The two spheres will reach the same potential so because of the symmetry of the situation it is not unexpected that they carry the same charge.
If they were not at the same potential there would be an E-field and charges would move.

With the one sphere inside the other it all depends on whether they are connected with a conductor or not.
If they are connected all the charge will finish up on the outside of the outer conductor.
If they were electrically isolated then the inner charge on the smaller sphere would induce an equal amount of charge of the opposite sign on the inside of the outer conductor and an equal amount of charge of the same sign on the outside of the outer conductor.

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