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bear with me, but i would like a definite answer, now, starting off the external charge density on the outer surface of sphere WILL be uniform by unique solution of Laplace equation and letting the sphere be huge, so, electric field due to outer surface charge=0, now, we come to the inner surface, where, if the charge was placed eccentrically then, there would be more induced charge of opposite polarity near the real charge if we chose sphere as cavity to cancel out the electric field of real charge so there MUST be NET force on the charge due to the internal cavity surface charge. -> right?

  1. if there was external electric field then the outer surface would cancel out the electric field inside the conductor at ALL the points again by unique solution if we let the cavity be very small hence, the answer shouldnt change-> right?

can somebody atleast tell me the exact answers of these questions and if my approach of using induced charges due the chrage itself to calculate force on itself is correct or not.. (dont be mislead by real charge...by it i mean the charge WE placed inside it)

extra if anybody has extra time- electric field inside cavity will be vector sum of the induced and real charge is there an image method for it?

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Regarding the first part, the induced charges can never be more than the charge placed and at best they will be equal in magnitude to the charge placed in the cavity( but opposite in sign). So the fields due to them will cancel out inside the conductor. Outside electric field will induce charges on the surface of the conductor but the direction of fields in this case will be additive at the surface unlike the previous instance where they cancel out. While discussing this we need to completely overlook the cavity charge as field due to it has been eliminated by the induced charge as discussed in the first para.

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