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Physics
Classical Physics
Electromagnetism
Grounded Means Zero Electric Potential: Exploring the Method of Images
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[QUOTE="BvU, post: 6851337, member: 499340"] A conducting grounded plane (infinitely large to keep thing simple) is an equipotential surface (otherwise charges would move until it was). If you place a charge ##q## above it at a distance ##d##, the plane still remains an equipotential surface, so things must happen: A nonzero surface charge distribution builds up on the top surface in such a way that the plane still remains an equipotential surface. The electric field lines just above the top surface have to be perpendicular to the plate (or else the charges would move along the surface). Since a configuration with an imaginary charge ##-q##, at ##-d## opposite the actual charge causes [U]exactly[/U] the electric field distribution in space that satisfies these conditions (zero potential at the surface and field lines perpendicular to the surface) AND a solution to the Laplace equation is unique, this mirror method is justified. With Gauss' theorem you can find the induced surface charge distribution. The integral of the surface charge over the entire top surface is ##-q##. NO ! A point charge is a singularity. The electric field and the potential at its exact position are infinite (in the convention that field and potential are zero at infinite distance from the point charge. I don't follow. How can what be zero ? Are you mixing up an equation for the potential field caused by a single point charge in space with a potential field (*) caused by a charge distribution on a plane ? (*) in the half-space above the plate ##\ ## [/QUOTE]
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Physics
Classical Physics
Electromagnetism
Grounded Means Zero Electric Potential: Exploring the Method of Images
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