A point charge is held at above a large earthed conducting plane

PHYSICS · Subjective · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Conductors, capacitance and boundary-value electrostatics · Conductors, capacitance and boundary-value electrostatics

The Boundary-Value Problem, Ch Uniqueness, images and the Green function of a region

Problem

A point charge q=4.0 nCq = 4.0\,\mathrm{nC} is held at d=2.0 cmd = 2.0\,\mathrm{cm} above a large earthed conducting plane. Find the error in the following working, and give the correct value of the electrostatic energy of the configuration. "The image charge −q-q sits a distance 2d2d from the real charge qq, so the pair's interaction energy is W=14πε0q(−q)2d=−q28πε0d.W = \frac{1}{4\pi\varepsilon_0}\frac{q(-q)}{2d} = -\frac{q^2}{8\pi\varepsilon_0 d}. Substituting the numbers gives W≈−3.6×10−6 JW \approx -3.6\times10^{-6}\,\mathrm{J}."

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