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Unsymmetrically Placed Charge in a Hollow Conductor
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May4-12, 01:38 PM
This doubt cropped up in my mind while going through my old electrostatics notes...
We consider a spherical shell with some thickness (so that two different charge distributions may be possible on the inner and outer surfaces of the shell) made of some conducting material, and electrically neutral (uncharged).
Now, when we place any charge at the center of the shell, then charges are developed on the inner and outer surfaces of the shell. These induced charges are supposed to ensure that there is no net electric field anywhere inside the conductor (between the inner and outer surfaces). We also observe, though, that once the induced charges are formed and have taken their place on the conductor's inner and outer surfaces, the charge at the center of the shell remains at equilibrium.
This makes sense, because the induced charges are supposed to ensure no net electric field in many concentric spherical surfaces (which constitute the volume of the shell) that are centered at the charge itself. So , when the induced charges remove any electric field from the concentric shells, it makes sense that the net field at the center of these shells comes out to be zero by symmetry.
But what if the charge was placed somewhere not so symmetrical within the shell? Would it experience no net force due to the induced charges which ensure no net electric field within the conductor (but not within the cavity, where our charge is asymmetrically placed)? What if the shell had some charge on it prior to the introduction of the charge in the cavity? And will electrostatic shielding take place for this charge, when the shell is placed in some external electric field??
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