Consider a large, thin, electrically neutral conducting

Chapter 26, Problem 26.81

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Consider a large, thin, electrically neutral conducting plate in the xy-plane at z = 0 and a point charge q on the z-axis at distance zcharge = d. What is the electric field on and above the plate? Although the plate is neutral, electric forces from the point charge polarize the conducting plate and cause it to have some complex distribution of surface charge. The electric field and potential are then a superposition of fields and potentials due to the point charge and the plates surface charge. Thats complicated! However, it is shown in more advanced classes that the field and potential outside the plate 1z 02 are exactly the same as the field and potential of the original charge q plus a mirror image charge q located at zimage = -d. a. Find an expression for the electric potential in the yz-plane for z 0 (i.e., in the space above the plate). b. We know that electric fields are perpendicular to conductors in electrostatic equilibrium, so the field at the surface of the plate has only a z-component. Find an expression for the field Ez on the surface of the plate 1z = 02 as a function of distance y away from the z-axis. c. A +10 nC point charge is 2.0 cm above a large conducting plate. What is the electric field strength at the surface of the plate (i) directly beneath the point charge and (ii) 2.0 cm away from being directly beneath the point charge?