A conducting object is in a region where external sources not shown in the figure and the induced surface charge density produce an electric field .
The induced surface charge density produces an electric field inside the conducting surface to cancel the electric field of the external sources, with the conductor absent. It also produces a perturbing electric field outside the surface.
Illustration of the proposed approach: The electric fields due to the surface charge density plus the external field are equivalent to the electric field distribution in Fig. 1, where .
A uniform charged sheet above an infinite conducting plane and the equivalent system of charges. The electric field inside the conducting plane is canceled if .
A point charge located near an infinite plane conductor and the equivalent system of charges. The electric field produced by the surface charge density cancels the electric field due to the point charge inside the conductor.
Conducting sphere placed in a uniform electric field and the equivalent system made up of the uniform external field plus a surface charge density . This surface charge produces a field inside the conducting surface that cancels the external electric field.
A point charge placed at inside a conducting spherical cavity of radius and the equivalent system of charges. The surface charge density produces the same electric field outside the cavity as a point charge placed at .
Neutral spherical conductor of radius and charge inside a cavity of radius .
Ring of total charge inside a conducting spherical cavity.
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